Only section 4 please

(a) Solve the ODE given by (5 marks) %(sin_1y) = $211, 39(0) = (l (b) Solve the ODE given by (5 marks} E = e? + xcosx gsinzr dc are?! (c) Solve the ODE given by (5 marks} if = 2m (.9 2e'\"2), y(0) = 1. SECTION 4: Numerical Methods for Differential Equations Show ALL working out [22 marks] (a) Write the differential equation in SECTION 3 (a) in the form (3 marks) 39' = FEW) 4 pages page 4 (b) Use the Euler method to approximate the solution to this ODE at MUS), take 3:, = 0.25 and work to 4 decimal places. (5 marks) (0) Comment on the result in the comparison to the exact solution. (2 marks) ((21) Use the RungeKntta fourth order method to solve the equation in SECTION 3 [c]. Pick h, = 0.05 and approximate y[U.1) working to four decimal places. (10 marks} (e) Comment on the results in comparison to the exact solution. (2 marks)