The following ODE governs the vertically the ODE given above and find a function for the vertical position of the ball y(t) and calculate the initial velocity of the ball at t = 0. y(t = 0.5) => y1 (t = 1.0) => y2 y(t = 1.5) => y3 (t = 2.0) => y4 ylt = 2.5) => y5 finite difference equation day dtª b) Discretize the ODE by hand using the finite difference method and end up with a linear system Ay = b where A is of size 5x5. (This means you should have 5 equations and 5 unknown y-positions of the ball. -> Position for the time levels [0.5, 1.0, 1.5, 2.0, 2.5]) de a =-9 le= ≈ -2y+y₁+1+1 (At)ª c) Row reduce the augmented matrix [A[b] in b) and convert it into Echolon form (upper triangular form in this case too.) and solve using Backward substitution d) Write a Matlab script that can generate the A matrix and the b vector and solves for the position of the ball at the time intervals [0.25, 0.50, 0.75, 1.00,..., 2.75] and plot t vs y