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

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

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(dy}{dx}=\frac{(y-sqrt(x^2+y^2)))/x

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

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

Solution steps

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

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}

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