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Math Help - Need help with this second order initial value problem

  1. #1
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    Need help with this second order initial value problem

    The problem is 6y''-5y'+y=0, y(0)=4, y'(0)=0

    I have found the two roots to be 1/2 and 1/3, so this gets us y=c_1e^{1/2t}+c_2e^{1/3t}

    It's after this where I get kind of lost.

    y(0)=c_1+c_2=4

    Where do I go from here?
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  2. #2
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    Quote Originally Posted by steph3824 View Post
    The problem is 6y''-5y'+y=0, y(0)=4, y'(0)=0

    I have found the two roots to be 1/2 and 1/3, so this gets us y=c_1e^{1/2t}+c_2e^{1/3t}

    It's after this where I get kind of lost.

    y(0)=c_1+c_2=4

    Where do I go from here?
    Use the other given boundary condition y'(0)=0 to get a second equation and then solve both equations simultaneously.
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