Question

For the differential equation, find the general solution:

`dy/dx = (1+x^2)(1+y^2)`

Answer 1

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

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

Integrating (i) both sides, we get

⇒ `tan^-1 y = x + 1/3 x^3 + C`

Which is the required solution.