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Math Help - Higher Order Complex Roots

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    Higher Order Complex Roots

    Find the general solution of the given differential equation:

    <br />
y^{6} - 3y^{4} + 3y'' - y = 0<br />
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    Quote Originally Posted by fudawala View Post
    Find the general solution of the given differential equation:

    <br />
y^{6} - 3y^{4} + 3y'' - y = 0<br />
    k^6 - 3k^4 + 3k^2 - 1 = 0

    (k^2-1)^3 = 0

    (k-1)(k-1)(k-1)(k+1)(k+1)(k+1)=0

    y=Ae^x+Bxe^x+Cx^2e^x+De^{-x}+Exe^{-x}+Fx^2e^{-x}
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