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}

y^{^{''}} - 3 y^{^{'}} - 4 y = 0, y (0) = a, y^{^{'}} (0) = - 20

\frac{d}{d x} (x^{\frac{8}{3}} - 20 x^{\frac{2}{3}})

\frac{d y}{d x} = y^{2} sin (x^{2}), y (- 2) = \frac{1}{3}

f (r) = π r^{2}

2 x x, at x = 1

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