Consider the ODE y'+12y=e-12t with y(0)=1.(a) Solve the ODE numerically by hand using Euler's method with t=1to approximate yatt=1,2,3,4,5. Show the calculations for all steps of the Euler solution.(b) Solve the ODE analytically by hand.(c) Plot the numerical and analytical solutions on the same axes for 0t5. Use symbols for thenumerical solution, and a line for the analytical solution (use sufficient points for the analyticalsolution tobe a smooth graph).(d) Determine the average absolute error of the Euler solution with t=1as:=1ni=1n|y(ti)Euler-y(ti)exact|=1ni=1n|yi,Euler-yi,exact|where nis the number of estimated values and iis the index of each estimated value and itscorresponding exact value. Briefly explain if the average absolute error is large or small.