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Find the constants for given IVP

  1. Feb 7, 2015 #1
    1. The problem statement, all variables and given/known data
    Untitled.png

    2. Relevant equations
    DifEqs

    3. The attempt at a solution

    y ' = 4C1e-4xSinX - 4C2e-4xCosX

    y'(0) = -1

    -1 = 0 - 4C2

    Therefore

    C2 = 1/4

    Not correct. What am I doing wrong?
     
  2. jcsd
  3. Feb 7, 2015 #2

    vela

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    You didn't differentiate correctly. You have to use the product rule.
     
  4. Feb 7, 2015 #3
    Sigh... obviously. Can't believe I just did that. Thanks!
     
  5. Feb 7, 2015 #4

    Svein

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    1. [itex] y=c_{1}e^{-4x}cos(x)+c_{2}e^{-4x}sin(x)[/itex]
    2. [itex]y'=c_{1}(-4e^{-4x}cos(x)-e^{-4x}sin(x))+c_{2}(-4e^{-4x}sin(x)+e^{-4x}cos(x)) [/itex]
    Now insert for y(0) and y'(0) and solve.
     
  6. Feb 7, 2015 #5

    HallsofIvy

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    Personally, I would find it easier to write the solution as [itex]y= e^{-4x}(C_1 cos(x)+ C_2 sin(x))[/itex].

    Then, by the product rule, [itex]y'= -4e^{-4x}(C_1 cos(x)+ C_2 sin(x))+ e^{-4x}(-C_1 sin(x)+ C_2 cos(x))[/itex].
     
  7. Feb 7, 2015 #6
    Yeah I got it dudes. I was just being stupid and completely forgot the product rule.

    Thanks
     
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