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Math Help - Wronskian Problem

  1. #1
    Member diddledabble's Avatar
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    Post Wronskian Problem

    I don't understand how to do these type of problems. Verify that the given function forms a fundamental solution set and then find the general solution using Wronskian.

     y'''-y''+4y'-4y=0
    Given {e^{x},cos2x,sin2x}
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  2. #2
    Senior Member
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    Wronskian - Wikipedia, the free encyclopedia

    W(e^x,\sin(2x),\cos(2x))(x)=\left|\begin{array}{cc  c}e^x & \sin(2x) & \cos(2x)<br />
\\e^x  & -2\cos(2x) & 2\sin(2x) \\e^x & -4\sin(2x) & \ -4\cos(2x)\end{array}\right|=10e^x

    Verifying that the Wronskian returns a nonzero determinant, these three functions represent linearly independent solutions. Thus the general solution is a linear combination of them:

    y(x)=Ae^x+B\sin(2x)+C\cos(2x)
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