What is the solution for (x/(x^2+y^2))dx-(y/(x^2+y^2))dy=0 ?

The solution for (x/(x^2+y^2))dx-(y/(x^2+y^2))dy=0 is y=sqrt(x^2+c_{1)},y=-sqrt(x^2+c_{1)}

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(x/(x^2+y^2))dx-(y/(x^2+y^2))dy=0

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

y = x^{2} + c_{1}, y = - x^{2} + c_{1}

Solution steps

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

Solve separable ODE:

y = x^{2} + c_{1}, y = - x^{2} + c_{1}

y = x^{2} + c_{1}, y = - x^{2} + c_{1}

y^{^{'}} = \frac{2}{3 x y + y}

x y \cdot y^{^{'}} = y - 1

x e^{x^{2}} + y y^{^{'}} = 0, y (0) = 1

\frac{d y}{d x} = - \frac{0.8}{cos ( y )}, y (0) = \frac{π}{4}

\frac{1}{1 - 2 y} d y = x d x

What is the solution for (x/(x^2+y^2))dx-(y/(x^2+y^2))dy=0 ?
The solution for (x/(x^2+y^2))dx-(y/(x^2+y^2))dy=0 is y=sqrt(x^2+c_{1)},y=-sqrt(x^2+c_{1)}