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=-1/(2e^{c_{1)}}+(e^{c_{1}}x^2)/2

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

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

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

Solution steps

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

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