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Homework Help: Find integrating factor and solve the equation 3

  1. Mar 28, 2010 #1
    y' + y = e^x ; y(0) = 1

    1st, i calculate the integrating factor...
    u(x) = e^x

    times the integrating factor with DE...

    y'e^x + ye^x = e^2x

    dy/dx e^x + ye^x = e^2x

    d/dx ye^x = e^2x

    ye^x = ∫ e^2x dx
    .........= 1/2 e^2x + C

    y = 1/2 e^x + C

    the problem here, i didn't get the answer given which is..
    y = 1/2 (e^x + e^-x)
     
  2. jcsd
  3. Mar 28, 2010 #2

    vela

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    You made an algebra mistake in the last step when solving for y.
     
  4. Mar 28, 2010 #3
    ok.. here is my mistake...
    ye^x = ∫ e^2x dx
    .........= 1/2 e^2x + C

    so.. when am i going to solve C value?
     
  5. Mar 28, 2010 #4

    vela

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    Up to there is correct. Your error was in the very last step you wrote when you solved for y.

    You can solve for C any time you want. Most of the time, it's done as the final step.
     
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