Question

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

Answer 1

Answer:

  see attached

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.)