So I'm supposed to verify the solution of the differential equation. The solution is y=e^(-x). The differential equation is 3y' + 4y = e^(-x). What is the problem asking me to do here?

Answer 1

plug in y to see whether it satisfies the differential equation

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

3y' + 4y = -3e^(-x) + 4e^(-x) = e^-x

so, it does satisfy it.

Answer 2

Oh, okay. I get it now. Thanks!