求下列微分方程的通解:[tex=3.071x1.357]m0sKckxx+jZ9iltApBtB27QYWFnv40zUd2jy6SC7LuRmlgTYsUQPuAc5EzcPMEu4[/tex].
此方程为不显含末知函数[tex=0.5x1.0]yBR4oiFoTexGaFalQ7m8kg==[/tex]的二阶微分方程,令[tex=2.143x1.357]HrIUUiwwAUgmfPgzzSx/9g==[/tex],则[tex=3.286x2.429]G9PKLA99GcFOtidK6KWEhkrb0AAvtNzGctem/HfpqGY51nMzbIajvBJkXTEitS2w[/tex],原方程可化为[tex=4.214x2.429]o3eWCNVo6rsRCTKw6Lqml5LVARRk0qInJtCgS2Yn/mg=[/tex],此为可分离变量微分方程,它的通解为[tex=3.0x1.214]cHVP88hM32KFtqDRnAA2iQ==[/tex],将[tex=2.143x1.357]HrIUUiwwAUgmfPgzzSx/9g==[/tex]代入,得[tex=10.571x2.643]joFwbCWxezua1X4SiQn0bC/G2yPTjC7WCEL8R9KiaTeQGxnvSkA58hPIWPBmXTEoukUvHNOvdueVSz0oDykZlA==[/tex].
举一反三
- 求下列微分方程的通解或满足给定初始条件的特解:[tex=5.214x1.357]TKVa+QfSJq+qPLObpUDqeZolDohIYgSgUh2jQm2x55U=[/tex],[tex=3.071x1.357]nzx9dL3PxNIYLyR8QiLBjw==[/tex]
- 求下列微分方程的通解:[tex=4.714x1.429]PHx3Vr0dFR2VA4jklKHr51xI90w+e+m6BmIrYYJz8/4=[/tex]
- 求下列微分方程的通解:[tex=4.214x1.429]eE9dXkpN2effVrNkAbXJmAfhrTcxtwjNNmZR6fEVsiDPD4FVC2xhREZna4MSAv7C[/tex]
- 求下列微分方程的通解:[tex=4.429x1.357]HZr1o9XmlNCVcm5lXbuOoclOP44fvikMFXOIw7OtTLU=[/tex]
- 求下列微分方程的通解.[tex=4.714x1.357]Ifkn8QhvAEOTqN3qC5TAEus+f683iloKcqaabkZJtOE=[/tex]
内容
- 0
求下列微分方程的通解:[tex=4.0x1.357]0impW2WklAhr9eiTopjCbHVSTf3RC7K3jqEEmP0ofwk=[/tex] .
- 1
求下列微分方程的通解: [tex=4.286x1.357]QmJ4zTKRbEaW9nTrORttlOCImb2CNjnzTdbybe4vlQ4=[/tex]
- 2
求下列微分方程的通解:[tex=6.643x1.429]LTMyH0WIzFUN0EHuFsgREnQKgexTsLjMeBZyz8IDCja3412pomMcUAWskqoUb+yu[/tex]
- 3
求下列微分方程的通解:[tex=4.429x1.429]4XDBu7mRoRcmkmv7MgmB65QNZg0sgo7cqCyCW9J6JHI=[/tex]
- 4
求下列微分方程的通解:[tex=4.857x1.429]eE9dXkpN2effVrNkAbXJmPQiiderz+rUkOrYtZ9FdOeE9cDb25MQWMMMiyTs+f9W[/tex]