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

Solution steps

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

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}

6 x^{2} + (x^{3} + 2) \frac{d}{d x} y = 0

\frac{d}{d x} (\frac{12}{x})

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\frac{d}{d x} (m x^{m + 5} + 6 x^{m} y^{n} + n x^{n + 3})

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