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Math Help - Finding a General Solution

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    Finding a General Solution

    Find the general solution of a 4th order linear homogenous d.e. with real number coefficients if two soultions are  y_{1} = xe^{-2x} and  y_{2} = xe^{x} .
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    Quote Originally Posted by tigergirl View Post
    Find the general solution of a 4th order linear homogenous d.e. with real number coefficients if two soultions are  y_{1} = xe^{-2x} and  y_{2} = xe^{x} .
    So you know that the auxillary equaiton is degree 4.

    y_1 represents the solution to a degree to of the form
    (m+2)^2 and y_2 is of the form (m-1)^2

    so the other two solutions are c_1e^{-2x} \text{ and } c_2e^{x}
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