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Question 3 (Learning Outcomes No.3 and 4) Find solution of the following 1st order ordinary differential equation with y(0) = 2. (a) (b) (c) (d) dy 1 3 #4 y = dx + 23 2 Find the general solution of the following 1st order ordinary differential equation. dy y + 1 = dx X Find the general solution to the following non-homogeneous 2nd order ordinary differential equation: d²y dy dx² dx For the following non-linear initial value problem dy dx 1 2y = 2x 1 = y - x² + 1, y (0) = 0.5 Find y(0.4) numerically with incremental step size h = 0.2 and accuracy to 5 decimals by (i) Euler Method. (ii) Improved Euler Method (iii) 4th order Runge-Kutta method (5 marks) (5 marks) (7 marks) (8 marks)