I'm in a numerical analysis class and I'm trying to approximate an initial value problem. I get the approximation using Forward Euler and other methods, but I'm not sure what the true answer is. I haven't done ODE's in a while.

Does anyone know how to solve the problem?

y'(t) = y - t^2 + 1, t in [0,2]

y(0) = 2

Thanks for any help in advance.