Question

verify that y=e^-x is a solution to the differential equation 3y'+4y=e^-x

Answer 1

do you know how to take the derivative (with respect to x) of e^-x ?

Answer 2

Yes, (-1/e^x)

Answer 3

@phi

Answer 4

I would leave it -e^-x (not that it matters too much)

replace y' with -e^-x
replace y with e^-x
and check that the left side matches the right side in your equaiotn

Answer 5

yes, I did that, then what

Answer 6

you are trying to see if both sides are the same when you plug in your y' and y with -e^(-x) and e^(-x) respectively

Answer 7

if both sides are the same then y=e^(-x) is a solution
if both sides aren't the same then y=e^(-x) is not a solution

Answer 8

I get -3/e^x +4e^-x = e^-x

Answer 9

I got the answer, thank you everyone