求微分方程的通解[y+(x^2+y^2)^1⼀2]dx-xdy=0

2024-11-28 07:40:41
推荐回答(2个)
回答(1):

[y+(x^2+y^2)^1/2]dx-xdy=0
>dy/dx=y/x+(1+(y/x)^2)^(1/2)
设z=y/x,则dy/dx=z+xdz/dx
>z+xdz/dx=z+(1+z^2)^(1/2)
>1/(1+z^2)^(1/2)dz=1/xdx
>z+(1+z^2)^(1/2)=cx
把y回代:
>y+(x^2+y^2)^1/2=cx^2
【OK?】

回答(2):

CCd
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