Solve the following differential equations:

Re - writing the equation as (1 – x²) dy = xdx(y² – y)

Now separating variable x on one side and variable y on another side, we have

Integrating both sides

Using identity:

and assuming x² = t

Differentiating both sides we get,

2 x dx = dt

Substituting this value in above equation

Replacing t by x²