The solution of the differential equation xdy−$$ydx=x2+y2dx$$ is

Correct option is 2y+x2+y2=c x2

Questions

The solution of the differential equation $x d y - y d x = (\sqrt{x^{2} + y^{2}}) d x$ is

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xy=x2+y2+c

y+x2+y2=c x2

x+x2+y2=c y2

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detailed solution

Correct option is B

dydx=y+x2+y2x=yx+x2+y2xdydx=yx+x1+yx2xdydx=yx+1+yx2put y=vxdydx=v+xdvdxv+xdvdx=v+1+v2xdvdx=1+v2⇒∫dv1+v2=∫dxx⇒lnv+v2+1=log⁡x+log⁡c⇒ln⁡yx+yx2+1=ln⁡|cx|⇒y+x2+y2=cx2

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The solution of the differential equation xdy−ydx=x2+y2dx is

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The solution of the differential equation $x d y - y d x = (\sqrt{x^{2} + y^{2}}) d x$ is