- #1

- 57

- 8

## Homework Statement

Particular solution of

y" - y' - 2y = e^(2x)

## Homework Equations

None

## The Attempt at a Solution

This makes no sense to me, why do I have to use the solution of the form

y(t) = cxe^(2x)

For the problem above, but when I switch the signs and it becomes

y" - y' + 2y = e^(2x) (notice the +2 in front of y)

The solution becomes y(t) = ce^(2x)

I get that it WORKS, but why? Am I seriously supposed to remember hundreds of forms for solutions when I solve these types of DE's or do I solve these with trial and error? It's ridiculously tedious trying several different forms just to realize it doesnt work at the end.