Consider the IVPs:
(A) y'+2y = 1, 0<t<1 , y(0)=2.
(B) y' = y(1-y), 0<t<1 , y(0)=1/2.
1. For each one, do the following:
a. Find the exact solution y(t) and evaluate it at t=1.
b. Apply Euler's method with Δt=1/4 to find Y4 ≈ y(1).
Make a table of tn, Yn for n=0,1,2,3,4.
c. Find the error at t=1.
2. Euler's method is obtained by approximating y'(tn) by a forward finite difference.
Use the backward difference approximation to y'(tn+1)...