Please code in matlab

1. This problem considers the seemingly innocent linear differential equation y(t) =-100y + 100t + 101 having general solution y(t) 1++ Ae-10 with integration constant A. a. Consider the class of initial value problems corresponding to the given differential equa- tion such that y(0) = 1 + C. Solve the initial value problem using your own foruard Euler method Matlab code with step size h = 0.05 over 0 t-1 for (i) C = 0, (ii) C = 0.01, and (iii) C =-0.01. Plot the numerical solution in each case. b. Consider the class of initial value problems corresponding to the given di tion such that y(0)-1+C. Solve the initial value problem using your own backward Euler method Matlab code with step size h = 0.05 over 0 t 1 for (i) C = 0, (ii) C 0.01, and (iii) C =-0.01. Plot the numerical solution in each case. In addition, plot the exact solution in each case. equa- c. Explain the differences in the numerical solutions garnered using the two methods in terms of (i) the numerical stability of each method and (ii) the underlying dynamics of the analytical solution