For the separating variables equation I have:

g(t) = 1 + y^2

h(t) = y + t^2

So

1/y+t^2 (dy/dt) = 1/y^2

(Integration) 1/y+t^2 (dy/dt) dt = (Integration) 1 +y^2 dt

(Integration) 1/y+t^2 dt = (Integration) 1 +y^2 dt

Arctan t = ????

What is the integral for 1 + y^2?

and am I along the right lines?