What is the solution for (dy)/(dx)=(y^3)/(x^2) ?

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

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(dy)/(dx)=(y^3)/(x^2)

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

y = - \frac{x}{2 ( - 1 + c _{1} x )}, y = - - \frac{x}{2 ( - 1 + c _{1} x )}

Solution steps

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

Solve separable ODE:

y = - \frac{x}{2 ( - 1 + c _{1} x )}, y = - - \frac{x}{2 ( - 1 + c _{1} x )}

y = - \frac{x}{2 ( - 1 + c _{1} x )}, y = - - \frac{x}{2 ( - 1 + c _{1} x )}

\int x^{3} (1 - x^{4})^{5} d x

\int (\frac{7}{1 - x ^{2}}) d x

\int (\frac{1}{1 + x ^{2}})^{2} d x

\int \frac{1}{( a ^{2} + x ^{2} )} d x

y^{^{'}} = \frac{( 1 - x - y )}{x + y}

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