Question

How to you find the general solution of `dy/dx=(x^2+2)/(3y^2)`?

Answer 1

`y(x) = root(3)(x^3/3+2x+C`

Explanation:

This is a separable differential equation, so we can proceed by separating the variables and integrating:

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

`3y^2dy = (x^2+2)dx`

`int 3y^2dy = int(x^2+2)dx`

`y^3 = x^3/3+2x+C`

`y(x) = root(3)(x^3/3+2x+C`