This is already in the required form (since the x-terms are together with dx terms, and y-terms are together with dy terms), so we simply integrate:

`inty^2dy+intx^3dx=0`

Giving:

`y^3/3+x^4/4=K`

This is the general solution for the differential equation.

We can continue on to solve this as an explicit function in x, as follows:

`y^3=3(K-x^4/4)`

`y=root(3)(3(K-x^4/4))`

Taking a typical constant value `K=5`, we have this solution graph:

510-5-101234-1-2-3-4-5-6-7-8-9-10xyOpen image in a new page

Typical solution graph `y=root(3)(3(5-x^4/4))`.