The solution of the differential equation $$xdydx=y+xey/x$$ is

Correct option is 1e−y/x+logx=c

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The solution of the differential equation $x \frac{d y}{d x} = y + x e^{y / x}$ is

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e−y/x+logx=c

ex/y+logy=c

logyx+exy=c

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detailed solution

Correct option is A

The given equation can be written as⇒dydx=yx+ey/x put y=vx then dydx=v+xdvdxv+xdvdx=v+ev ⇒∫e−vdv=∫dxx by variables separable⇒−e−v+c=log⁡x⇒e−y/x+log⁡x=c

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The solution of the differential equation xdydx=y+xey/x is

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The solution of the differential equation $x \frac{d y}{d x} = y + x e^{y / x}$ is