Show that the differential equation `y^(3)dy-(x+y^(2))dx=0` can be reduced to a homogenous equation.

Explanation

`y^(3)dy+(x+y^(2))dy=0`
or `y(dy)/(dx) = (x+y^(2))/(y^(2))`………….(1)
Lelt `y^(2)=t` or `2y(dy)/(dx)=(dt)/(dx)`
Equation (1) transforms to `(dt)/(dx) = 2(x+t)/t`
or `(dt)/(dx) = 2(x/t+1)`, which is homogenous.