prss.net
当前位置:首页 >> Dy yDx >>

Dy yDx

解:∵(y+x)dy-ydx=0 ==>ydy+xdy-ydx=0 ==>dy/y-(ydx-xdy)/y^2=0 (等式两端同除y^2) ==>dy/y-d(x/y)=0 ==>∫dy/y-∫d(x/y)=0 ==>ln│y│-x/y=ln│C│ (C是积分常数) ==>ye^(-x/y)=C ==>y=Ce^(x/y) ∴原方程的通解是y=Ce^(x/y)。

解:(常数变易法) 显然,y=0是方程的解。则设y≠0 ∵(x+y³)dy=ydx ∴ydx/dy=x+y³..........(1) 先解齐次方程ydx/dy=x ∵ydx/dy=x ==>dx/x=dy/y ==>ln│x│=ln│y│+ln│C│ (C是积分常数) ==>x=Cy ∴解齐次方程ydx/dy=x的通解是x=Cy (C是积分常...

如图所示:

用格林公式:奇点(0,0)不在积分域内. I = ∮L (ydx - xdy)/(x^2 + y^2) = ∫∫D [(x^2 - y^2)/(x^2 + y^2)^2 - (x^2 - y^2)/(x^2 + y^2)^2] dxdy = 0 用参数方程. { x = 1 + cost、dx = - sint dt { y = 1 + sint、dy = cost dt 0 ≤ t ≤ 2π ∮L (ydx...

有个简单的解法: xdy-ydx=y^2dy变形:(xdy-ydx)/y^2=dy 由于:d(x/y)=(ydx-xdy)/y^2 故:d(x/y)=-dy 通解为:x/y=-y+C 或:x=y(C-y)

∫2ydx+2xdy=∫2 d(xy)=2xy+C

解:∵(x+y)dy–ydx=0 ==>ydy-(ydx-xdy)=0 ==>dy/y-(ydx-xdy)/y^2=0 (等式两端同除y^2) ==>dy/y-d(x/y)=0 ==>ln│y│-x/y=ln│C│ (C是常数) ==>ye^(-x/y)=C ==>y=Ce^(x/y) ∴原方程的通解是y=Ce^(x/y)。

详细步骤写在纸上了

网站首页 | 网站地图
All rights reserved Powered by www.prss.net
copyright ©right 2010-2021。
内容来自网络,如有侵犯请联系客服。zhit325@qq.com