(b) Consider the ordinary differential equation: dx 2t² + x with x(0) = 4. dt (1) Use the ansatz x (t) = a eat-b(t² + 2t + 2) to find the analytical solution to this problem. (Do not solve the equation) (ii) Use the RK2 method to estimate the value of x(1) using steps of h = 0.5. Calculate the true relative error at t=1. Carry out all calculations to 6 decimal places. [12] (c) Consider the third-order differential equation: d³x d²x 3 -2xt = 3 with x (0) = 2, x'(0)=x"(0) = 0. dtª dt² Describe how you could solve this equation using the RK2 method, including supporting equations (without solving). [6] - 3