Solve using MATLAB:

1. Consider (t2+1)dtdy4ty=t,y(0)=1 (a) (2 pts) Solve this initial value problem and write its exact solution y(t). (b) (5 pts) Use Euler's method with h=0.01 to obtain a numerical solution u(t) at t=1 and plot the numerical solution u(t) (solid line) along with the exact solution y(t) (dashed line) for 0t1. (c) (3 pts) Compute the error e1 defined by e1=maxu(t)y(t)(0t1) for h=0.01,0.005, and 0.0025, and make a table showing the variation of e1 with h. What do you observe