Consider the initial value problem

$y^{\text{'}}(t)+cos(t)y^m(t)=2020e^{-t},$tin$(0,1),y(0)=0\mathrm{.}4.$

a$)(6$ pts$)$ For the numerical solution of problem $($P$1)$ write down the midpoint method

$($scheme$)$ with all details.

b$)(12$ pts$)$ Write a MATLAB implementation that gives the approximate solution of $($P$1)$

derived by the method constructed in part $($a$).$ Any unknown value will be asked from

the user.