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