求解下列常数系数线性微分方程 [tex=12.714x1.5]ijk+2eXKRxevaYdpvp2E68InmargkxqMscR/5HdHYThwL53jPfWuVQmJ0JuJXyFvOMPWFSLz1t/ILG06xZMV8A==[/tex]
这是欧拉方程，令[tex=2.714x1.143]bQndsR87w6jfxG2xt5Txuw==[/tex] ，代入方程得 [tex=9.357x2.5]U2YO7ZEYphrvDmbM7Ecrqcp/lIVz1ti0a8pNq7DNBqq3QmNnNrFGJHRkShl71UNG4lDxeEwCYEn/3ZnTN4nAcg==[/tex] （1） 特征方程 [tex=7.786x1.429]O6UPRZee+JMigjwLrYB7CeirRkOaCa5Ln820+B9lAKOrn8NLBSsJe16BNDdob3lO[/tex] 特征根[tex=7.214x1.286]htX6Trji9ItdWIJ8zUMov7lPnDqxQf6o7r2RgDmP8EqN34pcdqZcN0HcCnNW5ILO[/tex] (1)式的通解为[tex=13.214x1.5]ELEVmfHlJa/+kKf9RX5l59lLXNSOphY1oBG9Q4OmZYSC63z+eQp3BfpSEVp2nXnNsi0EtAELyrnrHLRgu8Ucmg==[/tex]所以所求方程的通解为[tex=15.857x2.357]j1PY+rQHOnT1HN6uimeZiT70apDglVSE4dRrEU456gFupKLkCl00Keqc7ajwkBWF8nL04D6ayhw5xXGGnMJliWDYUwAOwDpcC9bKNy4yltt/Rwz35K+It2Z5X9iP1nyx[/tex]
举一反三
- 求解下列常数系数线性微分方程[tex=12.5x1.429]eE9dXkpN2effVrNkAbXJmMUhT6uDNhFIlGSnl0yDSXkaZ9guifywmmNR4fRFc8tgrjKI60ZzZGuPyE6SLyhkWA==[/tex]
- 求解下列常数系数线性微分方程[tex=10.643x1.357]eE9dXkpN2effVrNkAbXJmEF4QAb7BXsNdYV1+CRuIXoC8ABKOFbQXZOpxk3Ug0GJOEcuKKyCIHbZbYEt+Rz3DA==[/tex]
- 求解下列常数系数线性微分方程：[tex=11.214x1.5]9v68vlqnF+kcDaktgaYEFZdsqY8Kc5MHTS+nHN76FMKc7Rstr4Imafw6XyhLcLGoV9k+N0r8j56KDxTdcu0pz1uhnXER5/6yLCikFtA104k=[/tex].
- 求解下列常数系数线性微分方程：[tex=8.071x1.5]CS4ykdUSgN3MwaDrJo4vJFXXPlWpR8KO/pdJ+JQcq0tjFEGuNT0JCZa9FsF8hMh+[/tex].
- 求解下列常数系数线性微分方程 [tex=9.286x1.429]DYUMX8H7hCBDfa6vYX3ilzlgupAN0QAb0/iNurLPO9dJ6NcD2mRIjNTiIAnddP3T[/tex]
内容
- 0
求解下列常数系数线性微分方程 [tex=9.643x1.357]eE9dXkpN2effVrNkAbXJmDx+h/50LyZCwjspCMcdYTINfjybGiVZt0GAJ1uYAzI0[/tex]
- 1
求解下列常数系数线性微分方程[tex=10.643x1.357]eE9dXkpN2effVrNkAbXJmIkD14dIYe9yFI8XDwQgkOUnOt/1iv4bPHnqdbIbFEyJOfysqzst/EIAN0TyliYjXQ==[/tex]
- 2
求解常系数线性微分方程 [tex=7.214x1.429]rjzw0bBUODiY66l+Mq83xAXwlAVED7uHGkHFCg7m+lX8E3suvLRzPfftKOPAIm+4Hq4gIYyxaAz3LuRirAOrHQ==[/tex]
- 3
求解下列常系数线性微分方程 : [tex=8.429x1.429]tRnrQWMhUlQy6Zihn7C/bF/4jIa0NmPn3uNAs5oxBDF+uDSpVFGiqJbcv1udjYZF[/tex]
- 4
求解变系数二阶线性微分方程[tex=10.786x1.429]WB8Nj6JgeOMcqnRQH9rBQZbcgp6WtJoAYMo9Ny8UKxQ8tctE3BeFNxuP98dnDPFgK5TVOGrPKo8LBx+Jyj5BUw==[/tex]