Finding C with inital condition, its wrong, any ideas why?

[mr_coffee]

Hello everyone, I'm having troubles figuring out this problem. The directions say:
It is easy to check that for any value of c, the function
y = ce^{-2x} + e^{-x}
is solution of equation
y' + 2y = e^{-x}.
Find the value of c for which the solution satisfies the initial condition y(3)= 8.


So I pluged in 4 for x and y(x) i plugged in 8 and got:
8 = ce^(-2*3) + e^-(3)
8 = ce^-6 + e^-3
8/(e^-6+e^-3) = c
c = 153 which is wrong
i also tried ln(153) = 5, which is also wrong. any idea where i screwed up, thanks!

 

[qbert]

...
y = ce^{-2x} + e^{-x}
...
Find the value of c for which the solution satisfies the initial condition y(3)= 8.
...
8 = ce^-6 + e^-3
8/(e^-6+e^-3) = c

ah, pesky algebra. 8 = c exp(-6) + exp(-3)
gives c = (8 - exp(-3))/exp(-6).

 

[mr_coffee]

Thanks a lot qbert, i don't know how i didn't see that hah! too much coffee tonight!