Solve the initial value problem?

Question

Solve the initial value problem y'=-y/2+t, y(0)=0 by the method of successive approximations.

Answer 1

You have to repeat the same steps as it shown in the previous problem. You will come up with Taylor expansion for function y(t) = 4e^-t/2 +2(t-2) which is the solution of your equation. You can checkm it by solving your euqation directly: y₀(t) = C e^-t/2 is the solution for homogeneous eqaution  y' = -y/2 and  y₁(t) = 2t-4 is the oarticular solution of your inhomogeneous equation. C = 4 is adjusted to satisfy to the initial condition y(0) = 0.