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

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

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

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

y = - \frac{x}{1 - x ^{2} + c _{1} x}

Solution steps

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

Solve separable ODE:

y = - \frac{x}{1 - x ^{2} + c _{1} x}

y = - \frac{x}{1 - x ^{2} + c _{1} x}

\frac{d y}{d x} = \frac{( x y - 4 x + y - 4 )}{( x y - 6 x - 3 y + 18 )}

\frac{d y}{d t} = 16 y

2 y y^{^{'}} = 12 t^{2}

\frac{d y}{d x} = \frac{y ^{3}}{x ^{4}}

\frac{d y}{d x} = - \frac{2}{4} x^{3} y^{8}

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