# Thread: Help for a friend

1. ## Help for a friend

My friend came to me with a problem from his differential equations class, and unfortunately I don't understand the directions. This is all he gave me, any help is much appreciated:

By substitution, determine the correct solution to the differential equation:

$y' = y + 13e^{-x}$

I can integrate and solve for y by completing the square but I'm not sure that's correct.

2. Re write

y ' - y = 13e^(-x)

multiply both sides by e^(-x)

e^(-x)y ' -e^(-x) y =13 e^(-2x)

Note the LHS is

d(e^(-x)y)/dx = 13e^(-2x)

Integrate

e^(-x)y = -13/2 e^(-2x) + C

y = -13/2 e^(-x) + C e^(x)