![](https://iknow-base.cdn.bcebos.com/lxb/notice.png)
用微分方程通解公式(公式在下图)求方程的解
3个回答
展开全部
(1) dy/dx = 1/(x+y), dx/dy - x = y,
x = e^(∫dy)[∫ye^(-∫dy)dy + C] = e^y[∫ye^(-y)dy + C]
= e^y[-∫yde^(-y) + C] = e^y[-ye^(-y) - e^(-y) + C]
通解 x = - y - 1 + Ce^y
(2) dy/dx - 2y/(x+1) = (x+1)^(5/2),
y = e^[∫2dx/(x+1)]{∫(x+1)^(5/2)e^[∫-2dx/(x+1)]dx + C}
= (x+1)^2[∫(x+1)^(1/2)dx + C]
= (x+1)^2[(2/3)(x+1)^(3/2) + C]
x = e^(∫dy)[∫ye^(-∫dy)dy + C] = e^y[∫ye^(-y)dy + C]
= e^y[-∫yde^(-y) + C] = e^y[-ye^(-y) - e^(-y) + C]
通解 x = - y - 1 + Ce^y
(2) dy/dx - 2y/(x+1) = (x+1)^(5/2),
y = e^[∫2dx/(x+1)]{∫(x+1)^(5/2)e^[∫-2dx/(x+1)]dx + C}
= (x+1)^2[∫(x+1)^(1/2)dx + C]
= (x+1)^2[(2/3)(x+1)^(3/2) + C]
本回答被网友采纳
已赞过
已踩过<
评论
收起
你对这个回答的评价是?
展开全部
enn...太难了
已赞过
已踩过<
评论
收起
你对这个回答的评价是?
推荐律师服务:
若未解决您的问题,请您详细描述您的问题,通过百度律临进行免费专业咨询
广告 您可能关注的内容 |