Chapter 26, Problem 4P

Solve the following initial-value problem over the intervalfrom $t=2\text{ to 3}$:

$\frac{dy}{dx}=-0.4y+e^{-2t}$

Use the non-self-starting Heun method with a step size of 0.5 and initial conditions of $y\left(1.5\right)=5.800007\text{ and }y\left(2.0\right)=4.762673$. Iterate the corrector to ${\epsilon }_S=0.1\%$. Compute the true percent relative errors ${\epsilon }_t$ for your results based on the analytical solution.