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

  1. Jan 14, 2006 #1
    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!
     
  2. jcsd
  3. Jan 14, 2006 #2
    ah, pesky algebra. 8 = c exp(-6) + exp(-3)
    gives c = (8 - exp(-3))/exp(-6).
     
  4. Jan 14, 2006 #3
    Thanks alot qbert, i don't know how i didn't see that hah! too much coffee tonight!
     
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