What is the solution for x^3ydx+x^2y^2dy=0 ?

The solution for x^3ydx+x^2y^2dy=0 is y=sqrt(-x^2+c_{1)},y=-sqrt(-x^2+c_{1)}

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x^3ydx+x^2y^2dy=0

x^{3} y d x + x^{2} y^{2} d y = 0

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

Solution steps

x^{3} y d x + 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}

\frac{d y}{d x} = 2 x y^{2} + \frac{5 y ^{2}}{x}

\frac{d y}{d x} y = ln (ln (x^{5}))

y^{^{'}} = - 3 x^{2} (y + 2), y (1) = - 1

\frac{d y}{d x} = (1 + y)

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

What is the solution for x^3ydx+x^2y^2dy=0 ?
The solution for x^3ydx+x^2y^2dy=0 is y=sqrt(-x^2+c_{1)},y=-sqrt(-x^2+c_{1)}