Question

How do you find all solutions of the differential equation `dy/dx=x^2y^2+x^2`?

Answer 1

`tan^(-1) y= x^3 /3 +C`

Explanation:

`dy/dx= x^2 (y^2+1)`

Thus `dy/(y^2+1) = x^2 dx`
Now integrate both sides,

`int dy/(y^2+1) = int x^2 dx`

`tan^(-1) y= x^3 /3 +C`