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

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

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x(dy)/(dx)=y-sqrt(x^2+y^2)

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

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

Solution steps

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

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