求微分方程[tex=7.357x1.286]CNsJwmk433hHLppsgOhxMQ68ZKuDcROTWA8EgiQM5AFLtcTYYSETjVSKqPtsi9lU[/tex]的通解。
解:此方程不显含[tex=0.571x1.286]XubEW9+1+hkJqH7jXe5MrA==[/tex],令 [tex=2.643x1.286]pCZPVGBKK5RW2fLoslnD0axvx+FfNxYgBI9g5uCc/qQ=[/tex], 则 [tex=3.714x2.643]Ei2PZQl92La73hUrygebc2PNhfqkzt410+IVCyYes0iAFQkOw75ptDF2Xtr9BSIyaRtuFhpjGNbkdg1NPENF6Q==[/tex],且原方程化为[tex=8.143x2.643]rOEnt1kdrLvx46cIfTyRkV4U3EuAiJ2q7CGl2OlnZTXcCAgKVTvIY+9ZjuZhOIrby0Ro3pXcta+bvKamfjIKxw==[/tex]。分离变量[tex=5.5x2.643]XekPSgTX3UIIsL5HMRMk/9n5/WM+G9AWBh6yf6XTZyALdCto2rHNmQg7IUnmzk1oOpua/mvBj31ScrOivprQKQ==[/tex],积分得[tex=11.571x2.357]0Jd07+iqmGp2nwHa61BlRPresnVe924sG0CK+YeEumiT0nuE556opc5xOQoQl2rxDxE+ojOmPrJCj57ZrZrdNw==[/tex],即 [tex=6.714x1.286]X9ajJhW3KY0VKyR64fZiLrjvpLyJPkwK/qSCcTF3LP8IVeSW9WIGZuZEXsDn4EBf[/tex],故[tex=8.143x1.786]e4py8FeBn0Iev6kVEs2dLaNRojsOwP9J2C1CKjjLjKN8CrNhtAf3oS0WXavfPqZ5[/tex]。取[tex=7.643x1.786]SPBXnvKZbKS20gqVrfKXZIwDUY84I4kRLQSiW/w6+zfWfn0FfRy+rJto83zg13JLeCY/ZrWDElcqsSCL/ztrIw==[/tex],分离变量并积分[tex=22.143x6.643]qeiYnKXLEhyhuGRg8yLtr4gHDn7LiV7OqzenkzquRUNLK5x4g8KDa+KFYEsEIeyOG6/JSdJZMSrPFLPXmjR4GZHDMpOn1+XDnA+HhMuNufVxD4AO2FHAbgPcGSMHu6R74OqbLVFEbzvkaVxx9FDizIahhoCUYgsSUn3XYA6fmUVEgHHXJ6xFfV8cdQ1YDYae2yP+umkllac7B39cxbIjEkjCPL3PUMW926OhJtBpRngkVTqWBjXoo5MfNcnJweVyxmeNNzUqVecVoM1hnj1g5iXNPKaC2hs5fp0n+ZOwanqTmeDOoeu1MDfcyQtX2kqAGGhG6OS9mLCbQaB9jKUmKKUhKcwQWuW7TYKK+vxcSujbKnovprJTfdIdZRboZVeHTZO/2UwE//gsd+PgstMQBe3dro+tAM9I30IdIF7AD4g=[/tex]即 [tex=11.357x2.571]+4/COEkujml0zdJ6FYz7L3B7nZqu7LGP2kOM+SKDLGbV1LV7XU5sKStRyLXN/w+nj69jGAt0wbfpawJFkkv2FrD3M5cjbZPIBtAzz1o6K9XpwVPJNvxpfHZP6H+dLZQi[/tex]。对于[tex=8.357x1.786]pH6TQ3XloXCyuTBIkOMF25js86HiR6ZtWt0V9ticGOb6udIp9xkboT4HZ2Lf/Iv8sL6Wl8anedSv9hNXAL033Q==[/tex], 可得相同的结果,故原方程的通解为[tex=12.357x2.5]+Itvj84G8BwZHw7iHt2sw7GF0m8p23hkw/vG1WNPd2Ly8qr4RznShKtzKPkArCKMi3rTvIO8Y53Q6kqO6dKgnUZ7FlMoo8aTsS5x4gIpFNyC+ouqa5dRF0IZvHooI6nD[/tex]。
举一反三
- 求函数[tex=7.357x1.286]/+XW7qMRK3D+OdKTuj6khRvFf6qmpp1KfZlTouyBSig=[/tex]的全微分 .
- 求微分方程[tex=4.857x1.286]Ei2PZQl92La73hUrygebc9rIJ7uCe10I8aWOrys81j34nFk4W32Dkg1WxA8RVwWo[/tex]的通解。
- 求微分方程[tex=4.714x1.429]eE9dXkpN2effVrNkAbXJmAfhrTcxtwjNNmZR6fEVsiAcGJIZL7kylQL6dVc6K+rI[/tex]的通解.
- 求微分方程的通解:[tex=4.714x1.429]eE9dXkpN2effVrNkAbXJmIaMnlWpJYU30cAYLWqAFLc=[/tex]
- 求微分方程[tex=6.5x1.286]upqC2BUtUv0lwZqEwo4GhzPN1TfU7+VS6hlrs3LSs0Y=[/tex]的通解。
内容
- 0
求微分方程 [tex=6.357x1.357]d1NLgtTQLz5ZKNXUeCaoko1b85cSlqkSpamSJAFugtY=[/tex] 的通解
- 1
求微分方程[tex=5.357x1.286]+/7MrLYBXhz05O8fENYs4lfbp+5DvgUoye433+G9zGEMusUosGaQajBEG5aERUgr[/tex]的通解。
- 2
求微分方程 [tex=3.857x2.429]s4QumE5pv31BDaGg1MTOdHLyE9aC3MZmRwFtEoQDEM8=[/tex]的通解。
- 3
求微分方程 [tex=9.357x1.357]BW13LybV3dhoeh+b44L3GjSwX0T16QFwtVgFzD09Uh4=[/tex] 的通解.
- 4
求微分方程 [tex=7.214x1.5]Ciihr42FDYc58KXZGHJAc4u63IYgPhDC0JoPgfANM9s=[/tex] 的通解