Question

Solve the following differential equation.

`dy/dx = x^2 y + y`

Answer 1

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

∴ `1/y dy = (x^2 + 1)dx`

Integrating on both sides, we get

` int 1/y dy  = int (x^2+1) dx`

∴ `log  | y | = x^3/3 + x + c`