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Homework Help: 2nd order linear differential equation (homogeneous)

  1. Oct 17, 2009 #1
    1. The problem statement, all variables and given/known data
    Solve 354y`` −692y` + 235y =0

    y(0) = 7
    y`(0) = 4

    2. Relevant equations

    3. The attempt at a solution
    First I divided the equation by 354 to get y`` - 1.56y` + 0.894y = 0.

    Then I found the roots of this to be 0.94, repeated twice.

    For repeated roots the solution looks like y= C1e0.94t + C2te0.94t

    Using the initial conditions, solve. You find that C1 = 7.

    y` = 0.94C1e0.94t + 0.94C2te0.94t + C2e0.94t. Plugging in t = 0 we find that C2 = -2.61.

    Therefore y = y= 7e0.94t -2.61te0.94t

    But this isn't the correct answer. Where did I go wrong?
    Last edited: Oct 17, 2009
  2. jcsd
  3. Oct 17, 2009 #2


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    Science Advisor

    You've rounded off incorrectly. -612/324 is 1.89 to two places, not 1.88. But I would be inclined to leave it as a fraction: 17/9. Are you allowed to do that?
  4. Oct 17, 2009 #3


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    Science Advisor
    Homework Helper

    Apart from the fact that you rounded nearly every single number, why isn't the solution correct?
    Because I got the same (up to rounding errors).
  5. Oct 17, 2009 #4
    Okay, I used fractions in my answer and that worked. Next time I'll be careful not to round carelessly... thanks!
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