Ensartet andre ordre differensialligninger med konstante koeffisienter.

{!LANG-c18bce9d2ae1355d6ffed5b723715e98!}{!LANG-0dcb2f674c410c00256d8cd9ef21a825!}

{!LANG-f1761702faae7f666e03d66a569c674a!}{!LANG-380b22ab95f129f3f073c73ad044e853!} {!LANG-4d2d7aeefd7dbed5af9f4dd6c499d5fa!}{!LANG-ae11eec729bd2bbb8bd24cb47ede3f63!}

{!LANG-c26ba904dd4392ecc55c93b0870d5d3e!} ,

{!LANG-4c3a86974d7e22b409d5f918893fc711!}

{!LANG-78319d9985dbbff82799a8014e749eb6!}

{!LANG-c67573f17edcfece38fbd9c5c5f8babd!}

{!LANG-47b33b7ee9410890b57728889c7141e3!}

{!LANG-64ec4d0c81b0eb95c1be10b9ab92298b!}<0) (c док-вом).

{!LANG-545dd5d85a0bfbff4c3d210e81d459bf!}

{!LANG-e18b4afb2c1339901ac2acc5b5f99732!}

{!LANG-be727f02c42d24a89806072a681bd176!}

{!LANG-ed2b65f8605978e4269b6a66c0f38d8b!}

2 ..

{!LANG-f22e286fe3a9f2eeb620700c40ccfd94!}

{!LANG-550bae88d95914b623291af2d685ee6d!}

{!LANG-38131fb2deff789e9150f33fa27df456!}

{!LANG-2f97e0d187c855a51c9ecf909dbacedc!}

{!LANG-ae64e7f400edcc8f484db72a3477bd17!} {!LANG-ccaf19382d125cb170a44942d94be621!}

16. {!LANG-fc2ec229e335ac23e40d09c4b1ba5141!}

{!LANG-275fede25a3e774a5f8a8bafb5baa4ba!}{!LANG-f6293fd92fc67750703cb052bd60baf4!}

{!LANG-f1761702faae7f666e03d66a569c674a!}{!LANG-cf8be13faffff355424274e7a15bfa5a!}

{!LANG-61ff7899135e87f33ce3cbe9f2c3badd!}

{!LANG-3b190d1ec846ae51d5602221287112ff!}

17. {!LANG-995cb887c951f8ef25111528570b2d3c!}

{!LANG-82437367b17364adeb4bb63ba4581fa0!}

Vurder metoden for å finne en privat løsning av ligning (7.1) i saken når den rette delen f (x) har et spesielt utseende.

{!LANG-52dca725917baf4341acd6b9472e6a1d!}

{!LANG-175b9257c84de7811b18e537875f818d!}

{!LANG-e86626f9fa18579b9332e2ac2fe17554!}

{!LANG-e3c282cd1f90cb59a9eb41ffddf4ba34!} , {!LANG-e15e745869378f3ba9dcaf9486a2a9b2!}

{!LANG-338a754d1b4bef9a5b6d7c7bde2bdc82!}

{!LANG-bde07efa351227863f305768f0095fe2!}

19. {!LANG-857092361b3694a7c0e77e2a3186accd!}

{!LANG-dae4fc44f1de0af89369b2a9b6c2b252!}

{!LANG-3a7237391a89aa03d422aa77579e3c82!}

{!LANG-9956068b980885622aee413894c5727c!}

{!LANG-8d57f7c6cf74b1cac54b7adccf6f158f!}

Skille dette uttrykket igjen.

{!LANG-40161f8d6e2fdd941296ef4bc2e0dd5b!}

{!LANG-488b58b84495cdc697b07d7ebc52072e!}

{!LANG-efd85eb964f01f62401f0ce1730c903c!}

(8.7)

{!LANG-823fb4553c75d56e17906ba650a426f4!}

{!LANG-8ecf555017aa4b8a649a30567396247e!}

{!LANG-b9bf6c3b865200c5f7e9cb6ac281ad31!}

1. {!LANG-a5d8abbfe0ad313211c35f4372c83565!}

{!LANG-48efe6abb660b9ec099cbf23f41f1c6c!}{!LANG-a8b39f988894f4de49125bca6a57bc1c!} . {!LANG-3283c08c12bc7b085bea7d802fddcea0!}{!LANG-4d40eebaf0056deaec22c3eaf6913990!} {!LANG-7e8da399049dc02cefa907f9d7db1a99!} {!LANG-2d36efa03a9dcd428e3eaeba0f011948!}{!LANG-f43271604f4339aacc123d98982a6fa0!} {!LANG-fe13119fb084fe8bbf5fe3ab7cc89b3b!} =1, {!LANG-fe13119fb084fe8bbf5fe3ab7cc89b3b!} =2,{!LANG-ac3153c52c792d635f076e16fe8854a6!} {!LANG-98d6d58b7422a6c5a0ac6d557afdf2ce!}

{!LANG-6fd39dbf6610a785d94da6fc7185ac06!} {!LANG-ce85f21731e2f3eacbf4358c6028a672!}:

{!LANG-bc449e93d833ffe414cd891fb289fcd1!} {!LANG-65db27307aa0cdf0b3c0323431e08a15!} {!LANG-01f30fc4282db781f4bd4fb743aff4a3!} {!LANG-65db27307aa0cdf0b3c0323431e08a15!} {!LANG-9a5b8c0b9870607d8857f2a347e77015!}

{!LANG-641b53424ccef1ca226cfe6e2e2ca458!} {!LANG-44bc121afdb8de395b727a503a28dc2b!}.

{!LANG-995ead9c99e7d28aaed58b87c6b6105e!}. {!LANG-158ee31f442d26fa74fa4f72f737d235!} {!LANG-8bd7ff73b30843d2a7704675547bf172!} {!LANG-abe42df72abeec88c6616e030eae4a62!}{!LANG-73d0ab4130a24fa78ad680806a46b151!} .

{!LANG-76f520d1fd2f679696b58e85f7b0d60d!}

{!LANG-031ecf16c27b396a1f07a7212c3e604c!}{!LANG-b07909535143b8ea4a9813998c6b8870!} {!LANG-ac3153c52c792d635f076e16fe8854a6!} {!LANG-5098a66e722648e1c2b9090413a9364c!} .

{!LANG-de52c66145fd2dea4f55c76e1c55bfc7!}

{!LANG-199df7bfdc93fbb8f3adf610ee428ed2!}

{!LANG-f5ca8b6a7b1a05259d38fc2a235fa0ff!}

{!LANG-e1441b3decf42420bc6a4d53b698c9b3!}

{!LANG-6fd3a3f6aa0ae736a500b1503b45d926!}

{!LANG-b185d8c06fe9079b1c62840b1644d879!}

{!LANG-c42d2f0e7d0ccdc5ad3e96f39dcafdc1!}

{!LANG-29005679db3f7d485d13c31d45781862!}

Definisjon av andre ordre LFD med konstante koeffisienter

{!LANG-37513dbe95756b4e45857119f41c884f!}

{!LANG-c69b41ead4029142496d6c85cc2fbc6c!}

{!LANG-cf8f2774c56f1c24982e7c8dd863e0d2!} {!LANG-72cfd272ace172fa35026445fbef9b03!} ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}{!LANG-952592319997d17fbf02b16e3cae2257!} {!LANG-537ac3fd61e64b26ee8f05ad7d15aafa!}

{!LANG-0cbcb7d748430af63cb20f7a9dfc8105!} {!LANG-72cfd272ace172fa35026445fbef9b03!} ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}{!LANG-5b7c692d3a8e469da16682eb7c62e297!}

{!LANG-d2e64cb42487b5eaf866b25cd96ff070!} {!LANG-72cfd272ace172fa35026445fbef9b03!} ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}{!LANG-e63d575a3a5cc648b9119803c1f57cdc!}

{!LANG-d086c0824c8f245ff03a86b46ef1388e!}

{!LANG-6e76850768b55406f0aa21bc21e5db21!}

{!LANG-50d9686ef633bb0067a4c4a03db1cb8e!} {!LANG-8f481e4e599bc55765ac488371af72fc!}

{!LANG-dcfb6aee6c89990aeadf5a639ee8e178!} {!LANG-105d3c7ff86658add5a3c1a3dbc856a0!}{!LANG-2823040a6f3c360745760e6f784e8d70!}

{!LANG-b4105a8365f96fbf4ef90b1000a2102e!} {!LANG-9d7bf075372908f55e2d945c39e0a613!}{!LANG-73365e38bf2b65234d77914e34d9fae0!} {!LANG-c3be117041a113540deb0ff532b19543!}

{!LANG-b25ab9e125f073a3ed347feaaf9b2f4d!}

{!LANG-b4105a8365f96fbf4ef90b1000a2102e!} {!LANG-ad9ca0c72bed9a352629893dadf74d1c!}{!LANG-f844bbeabbddb503066422f7d873fac6!} {!LANG-ad9ca0c72bed9a352629893dadf74d1c!}

{!LANG-f0afc69e5980e52b34a1ea794b6a39d4!}

{!LANG-b4105a8365f96fbf4ef90b1000a2102e!} {!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!}{!LANG-69af0ee752db4db3417c0a273135a970!}

{!LANG-013b5f1f0fc15adae47e51dabbf3525f!} {!LANG-3c7601b63e80a9c28693739dcc0fc65e!}, {!LANG-b40d6f36a280b3e0ee507558ea5fd376!}{!LANG-73365e38bf2b65234d77914e34d9fae0!} {!LANG-b40d6f36a280b3e0ee507558ea5fd376!}{!LANG-434b36164f6a08f1be397a0b867d0f5d!}

{!LANG-434caf2e4dff9e180372f180966a73e9!} {!LANG-ddb133ecd8f41185c0206490f1004cd4!}{!LANG-878a6f44d5762fbf90e11acb9711b46c!} {!LANG-b40d6f36a280b3e0ee507558ea5fd376!}, {!LANG-b40d6f36a280b3e0ee507558ea5fd376!}{!LANG-73365e38bf2b65234d77914e34d9fae0!} {!LANG-3c7601b63e80a9c28693739dcc0fc65e!}{!LANG-42af034cfa698ed08b302576654b2b8c!} {!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!} 2 , {!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!}{!LANG-46158bd6e89e282dca076b245c63dc9b!}

{!LANG-2515d395d0d4f03e48b103bc973b77b5!} {!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!}{!LANG-f844bbeabbddb503066422f7d873fac6!} {!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!}{!LANG-2fa9bcb5692c58b2d7abfa56a2184186!}

{!LANG-d6d568627f5571d56c6dca6906cf7438!}

{!LANG-42b222bc737425430dfbb35e24720e3c!}

{!LANG-c00391e74d87c2f6d5b7622158b7c2de!}. {!LANG-da2d94f29950cbd37bbbcabe318c754b!} {!LANG-bce5951fdc403e0f5b5757baa2d7d03d!} {!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!}{!LANG-f844bbeabbddb503066422f7d873fac6!} {!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!}{!LANG-ac139e6ca03deb39e9912e709beca3c5!}

{!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!}{!LANG-4b1d76016bad1c679b7ccf9e9254a4f7!} {!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!} 2

{!LANG-b4105a8365f96fbf4ef90b1000a2102e!} {!LANG-ad9ca0c72bed9a352629893dadf74d1c!}{!LANG-f844bbeabbddb503066422f7d873fac6!} {!LANG-ad9ca0c72bed9a352629893dadf74d1c!}{!LANG-266ea0094efc9da81ca60c36458247a4!}

{!LANG-250a36dc88011158bc40a1bccb2fcf39!}. {!LANG-925eef0d57503326f03a044a4817b265!} {!LANG-bce5951fdc403e0f5b5757baa2d7d03d!} {!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!}{!LANG-f844bbeabbddb503066422f7d873fac6!} {!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!}{!LANG-56762e60f5fa84f5a993c4c9298a04d0!}

{!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!} 1 = {!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!} 2 = {!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!}

{!LANG-feea5af42bf4d034c7c96702266e33f2!}

{!LANG-72dfaad34edb5036d0df616ff2910b29!}. {!LANG-a480e76ed52ce9e3f327036399baf364!} {!LANG-4e77b236e1ca6064a267f367ca067e01!}

{!LANG-0c940e3292c5d2b702d04c69c6e7d4ad!}

{!LANG-feea5af42bf4d034c7c96702266e33f2!}

{!LANG-787ebaf044e5ad674e3548b41f27e412!}

{!LANG-cfaf8c222ef1448c758b5d3f727a717b!}:

{!LANG-6e4d2547e77f1f287e47d6c6b85f73e5!} {!LANG-9d7bf075372908f55e2d945c39e0a613!}{!LANG-73365e38bf2b65234d77914e34d9fae0!} {!LANG-c3be117041a113540deb0ff532b19543!}{!LANG-769d1110d748ef9b0f56875690aaab89!}

{!LANG-11e689a53ed2c522c1c27e8d436169c5!}

{!LANG-64174be24bb46525700d75e366f77b1f!}

{!LANG-84a15f0fc1f99b180373d24d799eeb90!}

{!LANG-49c6faad5caf3cb75330002fbdca4a57!}

{!LANG-8b9dad138c91ed66b7b5041c5d401c84!}

{!LANG-9cbfdaff8c9a99f0f0df179ac28f6cf9!}

hvor, og - spesifiserte funksjoner, kontinuerlig på det gapet, som løsningen søkes på.

{!LANG-0b67a431e4c2d097af80b3c14ba753e2!}

{!LANG-6e89033a278e5a2b93e5a074e9c72f75!}

{!LANG-031ecf16c27b396a1f07a7212c3e604c!}{!LANG-be3dc88f812684935ad30bfcbbada524!}

{!LANG-c18bce9d2ae1355d6ffed5b723715e98!}{!LANG-d6d5e5cfc0ba1e91846d3ab1c12f5a0a!}

{!LANG-25f293ba28ca87447cec6bff331570bf!}

{!LANG-f1761702faae7f666e03d66a569c674a!}

{!LANG-18ec4b30d72c5f690fab912d2956e8c8!}

{!LANG-f95a7375ef21d59d0e4d7a2589678e0c!}

{!LANG-bb08b34c78f8977b89864a6bd641672a!}

{!LANG-47508535f3bafd1c8d72faf8d5dd248e!}{!LANG-00966f20b4e7ac5353c42bc802edb06a!}

{!LANG-f1f98985b0f8bfa141d9662b1b652661!}{!LANG-41b1dd3aace4571a9a2752760e0d7517!}

{!LANG-db29687b5f4a88e5e7788486e159d933!}{!LANG-215979c299a545c64c49b95f0dfb486c!}

{!LANG-48219a9b58c5d0441223cda0fa91099b!}

{!LANG-031ecf16c27b396a1f07a7212c3e604c!}{!LANG-fe36e9662deb7b6f8562384fe192a3c8!}

{!LANG-32107a4a20f414c62e0c837912d79b27!} {!LANG-504da9e2feda782bbf6a027d304fa972!} {!LANG-2080adf71e861ec05bdb0eabfc2465ca!} {!LANG-4aae6fa9befa307c25a57eaedf082a79!} {!LANG-55b61ca6ee97894e57458355f29484b0!}

{!LANG-6f3b9c94cfa667eadbed8cdf433abb91!} {!LANG-96d7c75c27b2eb955f67eb8461a2faf9!}

{!LANG-8410be9fe98225f385c7c29643f04a59!} . , , .

{!LANG-8923881a4ba0a7804b930195fb25e910!}

(3.2)

Denne formelen heter Liouville formel.

{!LANG-7d354636f185de64a65ce0a9b42320f7!}

{!LANG-c18bce9d2ae1355d6ffed5b723715e98!}{!LANG-317293c213bfd364c7c6bc6072161dc4!} {!LANG-340c07c03af6adecb42e9a8d15d003f9!}

{!LANG-f1761702faae7f666e03d66a569c674a!}

{!LANG-8f13149fd71e739c7c6cd202c9d05d21!} {!LANG-f16b9f568f878eca741af26e2fe6de7a!} {!LANG-6d34a24491c0b0ea9ca8c53dd1066f85!} {!LANG-4d2d7aeefd7dbed5af9f4dd6c499d5fa!}{!LANG-fe5776e15fa30acb6a1042167c42baf9!}

{!LANG-48e96be878cadf5aef649d38b2d84896!}

{!LANG-1c5f1426cc4a649c9de12493bf6a562a!}

{!LANG-74bd81d5e654968f807c40b50b7a05f8!}{!LANG-06dc58fecc3ca561e064b5bdfa25ac2e!} {!LANG-168b061752e5f691552cb56485c872e4!}

{!LANG-48ed7122e24b2d631b357767f3f248a8!}

{!LANG-a524b3a4a1f085ce65527833e238c11e!} {!LANG-354d0220b1f018975232a6a239d744a5!} {!LANG-c1efb175764f1ffc539512a26bb8b9fe!}

{!LANG-2e8ad1a157e165f8b8cb356bca7fd87f!}

{!LANG-50d4405253a23dbcff5aa9d0ea42d309!}

{!LANG-3dac8c25afe57bd26c0c74fa8f5697fc!}

{!LANG-85ba7042ad6b2ef11e33c27aa5772f26!}

{!LANG-0713cac1e739ad59a7ed9c234309f393!}

Dermed den andre rekkefølge ligningen https://pandia.ru/text/78/516/images/image015_28.gif "bredde \u003d" 34 "høyde \u003d" 25 src \u003d "\u003e. GIF" bredde \u003d "118" høyde \u003d " 25 src \u003d "\u003e. Gif" bredde \u003d "117" høyde \u003d "25 src \u003d"\u003e. Gif "bredde \u003d" 34 "høyde \u003d" 25 src \u003d "\u003e.

{!LANG-3b4ea6734620acdd1ca16a9d414f9262!}{!LANG-ef22f856eccbfb0dc39b726826bb0b9a!}

{!LANG-5d68720db4c2be6c1b433ec1abae9533!}

{!LANG-d9592b22319d804dc2f38a915f28817b!}

{!LANG-48ed7122e24b2d631b357767f3f248a8!}

{!LANG-d95a762d993b0e02db18bf9e2a198ff9!}

{!LANG-6e8daabe3386198cba04245b5d3b0d79!}

{!LANG-26dafcfd22c12c31ad9dbadb42495c6e!}

{!LANG-f360cd361fe59b92d021910929c72005!}

{!LANG-969b57cd6baf56df0476ab23a3bb693e!}

{!LANG-c18bce9d2ae1355d6ffed5b723715e98!}{!LANG-cd2706de08cef8c37176b1483e5b60f2!}

https://pandia.ru/text/78/516/images/Image076_10.gif "Bredde \u003d" 182 "Høyde \u003d" 25 SRC \u003d "\u003e vil også være en løsning på denne ligningen.

{!LANG-f1761702faae7f666e03d66a569c674a!}

{!LANG-3ed73a4733a6e9ee50ff83f5a31f2b81!}

{!LANG-71f997075820176e69f7b0ae325620d7!}

{!LANG-b19107eb18b64cbf069ee8362fd25732!}{!LANG-bd62280a7be3e03258dd0ece1be43922!}

{!LANG-db29687b5f4a88e5e7788486e159d933!}{!LANG-54598acd080f4842049344ce3c86e91a!}

{!LANG-48219a9b58c5d0441223cda0fa91099b!}

{!LANG-031ecf16c27b396a1f07a7212c3e604c!}{!LANG-1aa533b670b87add7de6a7f0a26d2374!}

{!LANG-7b5a8b3210e8eb93baa24e4c15cc9717!}

{!LANG-d4699449c0586fc9339d4bec81c6268f!}

{!LANG-7d354636f185de64a65ce0a9b42320f7!}

{!LANG-c18bce9d2ae1355d6ffed5b723715e98!}{!LANG-1414e285564dfa5ab9975a422d4e8160!}

{!LANG-536161bc524e5d456a99c97919ac8722!}

https://pandia.ru/text/78/516/images/image116_7.gif "bredde \u003d" 138 "høyde \u003d" 25 src \u003d "\u003e. GIF" bredde \u003d "19" høyde \u003d "25 src \u003d"\u003e. GIF "WIDTH \u003d" 69 "Høyde \u003d" 25 SRC \u003d "\u003e. GIF" Bredde \u003d "235" Høyde \u003d "48 SRC \u003d"\u003e .gif "bredde \u003d" 143 "Høyde \u003d" 25 SRC \u003d "\u003e (5 .gif "bredde \u003d" 77 "høyde \u003d" 25 src \u003d "\u003e. I henhold til forrige avsnitt er den totale avgjørelsen fra 2. ordre lett bestemt hvis to lineært uavhengige private løsninger av denne ligningen er kjent. En enkel metode for Å finne private løsninger ligning med konstante koeffisienter foreslått L. Euler..gif "bredde \u003d" 25 "høyde \u003d" 26 src \u003d "\u003e, vi får en algebraisk ligning, som kalles karakteristisk:

{!LANG-8e4f251009855558eacfc2caff07cef5!}

{!LANG-7b1a523c8310d08f9e8a84d615e4bbe4!}

{!LANG-c38243f486c9364f10ecc9eb0975a9a3!}

{!LANG-68febf9f1877f84a105bb112d81d9d0c!}

{!LANG-5208ef281472bb6939e784374af32801!}

og hvilken som helst privat løsning https://pandia.ru/text/78/516/images/image166_6.gif "bredde \u003d" 87 "høyde \u003d" 25 src \u003d "\u003e vil være løsningen av ligning (6.1) .. GIF" bredde \u003d "272" høyde \u003d "25 src \u003d"\u003e f (x).

{!LANG-b0a2301491d43f0b704c0b38f45ea9cc!}

{!LANG-c374de4e9623adf9c7c9d180c8665656!}

{!LANG-96146058201a9ff35fb2142cf0305a77!}

{!LANG-941c5386faa2129bf3505c06e652707f!}

{!LANG-0713d2dbb8303efbbca17db2a42cfeb9!}

{!LANG-f9f1192c2355cb478e77583d42d9ecc2!}

{!LANG-4d411b08b1827597e280d81822b8cd00!}

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{!LANG-728fa70794635a7b70961a4841cee921!}

{!LANG-48a2c6e1cf3351ee948f00711eb76d45!}

{!LANG-93a44845c2ea07735751ba50e0a62c69!}

https://pandia.ru/text/78/516/images/image190_5.gif "bredde \u003d" 11 "Høyde \u003d" 25 src \u003d "\u003e. GIF" bredde \u003d "423" Høyde \u003d "25 SRC \u003d"\u003e,

{!LANG-48ed7122e24b2d631b357767f3f248a8!}

{!LANG-e7a3f56a751d8909b1595f38f4283048!}

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{!LANG-a33f6364fcffdd3f58115141494362ac!}

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{!LANG-d81869530ca5e621a1619b0c0019dd72!}

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{!LANG-48ed7122e24b2d631b357767f3f248a8!}

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{!LANG-7acdc6de833f038e2551f9b06b6dfded!}

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{!LANG-fc20d1ca259e8b96094aefb3bb04c7be!}

{!LANG-3259235f0606875bf544542cd9d5565f!}

{!LANG-f0a447e1d015131254356163861b509b!}

{!LANG-e8fd404654265de9e8f9b50881416913!}

{!LANG-1ded7dab9d135a4274162eb09ceabaaa!}

https://pandia.ru/text/78/516/images/image259_2.gif "bredde \u003d" 17 "høyde \u003d" 25 src \u003d "\u003e. I uttrykket (7..gif" bredde \u003d "121" høyde \u003d "25 src \u003d"\u003e.

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{!LANG-02436a5d5f128c8a32f0f9c535a4f8d2!}

{!LANG-4691963b15a9844ab2bbd879b625c817!}

{!LANG-dae4fc44f1de0af89369b2a9b6c2b252!}

{!LANG-3a7237391a89aa03d422aa77579e3c82!}

{!LANG-b15b949e5d0987af963e11bceb600341!}

{!LANG-ff00aa6d289a710df0d11242a9f44a42!}

{!LANG-7594386250e329315c940df3dda5a020!} {!LANG-e0bd34d5a6a30f15350680f97de05474!}

{!LANG-009520053b00386d1173f3988c55d192!}"" + {!LANG-9d7bf075372908f55e2d945c39e0a613!}({!LANG-401b30e3b8b5d629635a5c613cdb7919!}){!LANG-009520053b00386d1173f3988c55d192!}" + {!LANG-c3be117041a113540deb0ff532b19543!}({!LANG-401b30e3b8b5d629635a5c613cdb7919!}){!LANG-009520053b00386d1173f3988c55d192!} = {!LANG-9a8ad92c50cae39aa2c5604fd0ab6d8c!}({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) ,

{!LANG-b4105a8365f96fbf4ef90b1000a2102e!} {!LANG-009520053b00386d1173f3988c55d192!}{!LANG-7b131209e66a2491cc2174a3fb2a56c5!} {!LANG-9d7bf075372908f55e2d945c39e0a613!}({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) , {!LANG-c3be117041a113540deb0ff532b19543!}({!LANG-401b30e3b8b5d629635a5c613cdb7919!}{!LANG-d6faea4e44086b30bfeaf1b7fafadcdc!} {!LANG-9a8ad92c50cae39aa2c5604fd0ab6d8c!}({!LANG-401b30e3b8b5d629635a5c613cdb7919!}{!LANG-9065d28709554f5dd48621408c845fb0!} {!LANG-ec09c5bfd92a19dbd67d88b567e19489!}) .

{!LANG-d5f46bfc67579450c90a92be1fd8a3d2!} {!LANG-9a8ad92c50cae39aa2c5604fd0ab6d8c!}({!LANG-401b30e3b8b5d629635a5c613cdb7919!}{!LANG-d98629324d59ba1543d868cf2c9f8393!} {!LANG-aecfd9b911909356b21fce8f3249fa1a!} {!LANG-a12b23f876a9d5c9be94a5dad9e96bc9!} {!LANG-9a8ad92c50cae39aa2c5604fd0ab6d8c!}({!LANG-401b30e3b8b5d629635a5c613cdb7919!}{!LANG-29873c55451ea3126302c5d9785cb103!}

{!LANG-437fb187eb562a5aeba0048424f4e9e3!} {!LANG-009520053b00386d1173f3988c55d192!}"" :

{!LANG-009520053b00386d1173f3988c55d192!}"" = −{!LANG-9d7bf075372908f55e2d945c39e0a613!}({!LANG-401b30e3b8b5d629635a5c613cdb7919!}){!LANG-009520053b00386d1173f3988c55d192!}" − {!LANG-c3be117041a113540deb0ff532b19543!}({!LANG-401b30e3b8b5d629635a5c613cdb7919!}){!LANG-009520053b00386d1173f3988c55d192!} + {!LANG-9a8ad92c50cae39aa2c5604fd0ab6d8c!}({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) .

{!LANG-e1061b533dcc93d4fda004ebfc44cc93!} {!LANG-04d3ad70ba62a554d9a4f8014c0be5f8!} .

{!LANG-b4da4f1e5e65ce9c503ed2fea4b4f74e!}

{!LANG-e37199a3ff6e7dd496548cdf06a472aa!}

{!LANG-6515a1f1444ee93b1f53b23d3e7017c9!} {!LANG-009520053b00386d1173f3988c55d192!}1 ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) {!LANG-ef0c2fdd3aa4779ee5430927aa53641e!} {!LANG-009520053b00386d1173f3988c55d192!}2 ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) {!LANG-31b7684a2f589a0cf4ca44902ac3b066!}

1) {!LANG-009520053b00386d1173f3988c55d192!}1 ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) + {!LANG-009520053b00386d1173f3988c55d192!}2 ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) {!LANG-fdc09e2a63044ec02815cc397a9ea75e!}

2) {!LANG-4b11370c9c256092dc7507732f7b4288!}1 ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) {!LANG-6612b069541ea61ec545b8bf801033c7!} {!LANG-b39bfc0e26a30024c76e4dcb8a1eae87!}{!LANG-1470f13541cce31e23870410ecadee33!}

{!LANG-679d4c7459ccf22a9dfa40b9aeb5d822!}

{!LANG-b39bfc0e26a30024c76e4dcb8a1eae87!}1 {!LANG-009520053b00386d1173f3988c55d192!}1 ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) + {!LANG-b39bfc0e26a30024c76e4dcb8a1eae87!}2 {!LANG-009520053b00386d1173f3988c55d192!}2 ({!LANG-401b30e3b8b5d629635a5c613cdb7919!})

{!LANG-d447b1f537159040df6d4c482984363a!}

{!LANG-b3dacb8d9a3eb9d7b3f92e2b5c89c447!} den generelle løsningen av den lineære homogene differensielle ligningen i den andre rekkefølgen {!LANG-b39bfc0e26a30024c76e4dcb8a1eae87!}1 {!LANG-ef0c2fdd3aa4779ee5430927aa53641e!} {!LANG-b39bfc0e26a30024c76e4dcb8a1eae87!}2 {!LANG-9edb998a74304bc69554142c7431d7e4!}

{!LANG-3ad26b6c73d6416ab67455417b077eaa!} {!LANG-49f5a79295cd52c87b9e4f096969c470!} {!LANG-009520053b00386d1173f3988c55d192!}1 ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) {!LANG-ef0c2fdd3aa4779ee5430927aa53641e!} {!LANG-009520053b00386d1173f3988c55d192!}2 ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) .

{!LANG-48d11b33bdb6ab50756c3fce1dfdb2f5!}

{!LANG-dbe8cecfc9336b53a2d2ff4face87920!}{!LANG-cff1db4deab59a6c799be92e9964b1bb!} {!LANG-b39bfc0e26a30024c76e4dcb8a1eae87!}1 {!LANG-009520053b00386d1173f3988c55d192!}1 ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) + {!LANG-b39bfc0e26a30024c76e4dcb8a1eae87!}2 {!LANG-009520053b00386d1173f3988c55d192!}2 ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) {!LANG-ff670d6829a88c2917c1a23b0dc71779!} {!LANG-009520053b00386d1173f3988c55d192!}1 ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) {!LANG-ef0c2fdd3aa4779ee5430927aa53641e!} {!LANG-009520053b00386d1173f3988c55d192!}2 ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) {!LANG-feaa987fc1fb22f088cb747cd098a636!}

{!LANG-ceac657d9ba17dfe6044b7e0c95bb3b8!}{!LANG-1e9a80318f843624d76eaa707fd0adc9!} {!LANG-009520053b00386d1173f3988c55d192!}1 ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) {!LANG-ef0c2fdd3aa4779ee5430927aa53641e!} {!LANG-009520053b00386d1173f3988c55d192!}2 ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) {!LANG-201ceb40f31463aa7f6ac62672b30aad!}

{!LANG-009520053b00386d1173f3988c55d192!}1 ({!LANG-401b30e3b8b5d629635a5c613cdb7919!})/{!LANG-009520053b00386d1173f3988c55d192!}2 ({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) = {!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!} ; {!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!} = {!LANG-7abe721ec8acd29dcd135c6f2ccd4f9e!} ; {!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!} ≠ 0 .

{!LANG-0523aee256bcc63c84348ddd9f158ffd!} {!LANG-03f86d939c818d4858b6f70ddec66f3d!} {!LANG-f14e837db317a2bba9826144e7831b51!}({!LANG-401b30e3b8b5d629635a5c613cdb7919!}) :

{!LANG-9e890fb3760b8e4168e17f55c1c89503!} {!LANG-7ddffacd4aa38b78ddf1c0975c78f861!}

{!LANG-3b4ea6734620acdd1ca16a9d414f9262!}{!LANG-5fe7dcb29fc279b39cd62d219e5017f3!}

{!LANG-7da24dbbae084b35515bc258fca7b123!}

{!LANG-cfa0ba435d08ee4cbde7b76823c94003!}

{!LANG-ccc04ad1195b2b9d1947d473418f0c16!}

{!LANG-a9c57a8ea1ee0be82908a7193ab5baff!}

{!LANG-4c75a63a00c32054cee644bdce734e46!} {!LANG-e0bd34d5a6a30f15350680f97de05474!}

{!LANG-009520053b00386d1173f3988c55d192!}"" + {!LANG-9a4cf857b2924573b9f8cededcdcbded!}" + {!LANG-71c22d18fc76895f88cb2757804b94b4!} = 0 ,

{!LANG-b4105a8365f96fbf4ef90b1000a2102e!} {!LANG-9d7bf075372908f55e2d945c39e0a613!}{!LANG-7153e3894c754d5b6604e08eefccfd7a!} {!LANG-c3be117041a113540deb0ff532b19543!}{!LANG-b9b55980561a48b71d9b92f17bad36cc!}

{!LANG-a08897dd99057711989638a3c21480e1!}

{!LANG-77dd0cdf5edd455f234ce6498a24f417!} {!LANG-d5833e69265c084b24c3c31cc5c48277!} {!LANG-2b065f923297192b933b7d955635ee42!}

{!LANG-ccc87e7257869ad33a6a0bd9e28a4ae4!}² + {!LANG-0945896953fdc6b4b6538a9cd09b8bf0!} + {!LANG-c3be117041a113540deb0ff532b19543!} = 0 ,

{!LANG-37177c61e7e504b166a5f1e4af1b6f6d!}

{!LANG-fb93ec234b93523ce3209f8dc6b60c65!} {!LANG-3c7cc5d40039388ba9bc1f75418592c0!} hvem vil nå skille seg.

{!LANG-d8ffc3b5f1621d9acec6802e1aff8666!}

{!LANG-7e614d10ddcd85c4b85d138b6c54a486!}