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Solve IVP 2nd order differential equation

  1. Oct 7, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the particular solution of the linear, homogeneous, 2nd order differential equation: y'' - 2y' + 2y = 0, given the solutions y1 = (e^x)*(cos x), y2 = (e^x)*(sin x), y(0) = 0, y'(0) = 5.

    2. Relevant equations

    3. The attempt at a solution
    How do I begin? I'd really appreciate any help! Thank you.
  2. jcsd
  3. Oct 7, 2010 #2


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    Science Advisor
    Gold Member

    Your general solution (before applying initial conditions) is a general linear combination of your two given solutions:
    y = A y1 + B y2.
    You then substitute in your two initial conditions and solve for the arbitrary constants A and B.
  4. Oct 11, 2010 #3
    Ah, thank you for putting it so short and clearly :)
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