What is the solution for (y-sqrt(x^2+y^2))dx-xdy=0 ?

The solution for (y-sqrt(x^2+y^2))dx-xdy=0 is y=-(x^2}{2e^{c_{1}}}+\frac{e^{c_{1}})/2

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(y-sqrt(x^2+y^2))dx-xdy=0

(y - x^{2} + y^{2}) d x - x d y = 0

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

Solution steps

(y - x^{2} + y^{2}) d x - x d y = 0

Solve using substitution:

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

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

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What is the solution for (y-sqrt(x^2+y^2))dx-xdy=0 ?
The solution for (y-sqrt(x^2+y^2))dx-xdy=0 is y=-(x^2}{2e^{c_{1}}}+\frac{e^{c_{1}})/2