What is the solution for xdy-ydx=sqrt(x^2+y^2)dx ?

The solution for xdy-ydx=sqrt(x^2+y^2)dx is y=-1/(2e^{c_{1)}}+(e^{c_{1}}x^2)/2

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xdy-ydx=sqrt(x^2+y^2)dx

x d y - y d x = x^{2} + y^{2} d x

y = - \frac{1}{2 e ^{c_{1}}} + \frac{e ^{c_{1}} x ^{2}}{2}

Solution steps

x d y - y d x = x^{2} + y^{2} d x

Solve using substitution:

y = - \frac{1}{2 e ^{c_{1}}} + \frac{e ^{c_{1}} x ^{2}}{2}

y = - \frac{1}{2 e ^{c_{1}}} + \frac{e ^{c_{1}} x ^{2}}{2}

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What is the solution for xdy-ydx=sqrt(x^2+y^2)dx ?
The solution for xdy-ydx=sqrt(x^2+y^2)dx is y=-1/(2e^{c_{1)}}+(e^{c_{1}}x^2)/2