
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:
$\displaystyle y' = y + 13e^{x}$
I can integrate and solve for y by completing the square but I'm not sure that's correct.

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)