Question

Y'+2y = 5-e^(-4x), y(0)=-11

Use Euler's Method with a step size of h = 0.1 to find approximate values of the solution as x= 0.1, 0.2, 0.3, 0.4, and 0.5. Compare them to the exact values of the solution at these points.

Answer 1

see attached

Step-by-step explanation:

A differential equation solver says the exact solution is ...

y = 5/2 -14e^(-2x) +1/2e^(-4x)

The y-values computed by Euler's method will be ...

y = ∆x·y' = 0.1(5 - e^(-4x) -2y)

The attached table performs these computations and compares the result. The "difference" is the approximate value minus the exact value. (When the step size is decreased by a factor of 10, the difference over the same interval is decreased by about that same factor.)