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

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

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y^'=(y+sqrt(x^2+y^2))/x

y^{^{'}} = \frac{y + x ^{2} + y ^{2}}{x}

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

Solution steps

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

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}

y = 2 x^{3} + 3 x^{2} - 12 x + 6

\int \frac{1}{9 x ^{2}} d x

\frac{\partial}{\partial x} (x^{2} y z^{3} (x - 10 y))

\int arcsec (4 x) d x

(e^{t} x + 1) d x

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