dx2 = 2y 8x + 72, 1. Solve the following ODE using shooting method, after splitting the equation use Explicit Euler method (step size, h=1) to perform the numerical integration of the two IVPs simultaneously day y(0) = 0, y(9) = 0 2. Consider the following boundary value problem day dx2 = y, y(0) = 0, y(2) = 1 Solve using the shooting method and perform the numerical integration with the simultaneous initial value problems using Heun's method with step size, h=0.1 3. Solve the following boundary value problem using finite difference method day dx = -y, y(0) = 0, y(1) = 1, h = 0.25 Answer: y1 = 0.2943, y2 = 0.5701, y3 = 0.8108 4. Solve the following ODE using finite different method, day = x4(y - x) dx2 With the following boundary conditions y(0) = 0, y(1) = 2 And a step size, h = 0.25 Answer: y = 0.3951, y2 = 0.8265, y3 = 1.3396