A. Write down the exact solution to the initial value problem du/dt = 27 u, u(0) = 13 .
b. Suppose you make the approximation u(0) = .3333. At what point does your solution differ from the true solution by 1 unit? by 1000 units?
c. Answer the same question if you also approximate the coefficient in the differential equation by du/dt = .2857 u.