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Math Help - Can anyone help me get to the next step in second order equations?

  1. #1
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    Can anyone help me get to the next step in second order equations?

    y''-3y'-10y=0, y=1, y'=10 at x=0

    I know how to get it to the general equation correctly, but where do I go from there in these types of questions?

    The general form is y=C1e^-2x+C2e^5x

    Do I plug in x=0? That would leave C1+C2=10 which doesn't seem right....

    I need to get to y(x)=__________
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by operaphantom2003 View Post
    y''-3y'-10y=0, y=1, y'=10 at x=0

    I know how to get it to the general equation correctly, but where do I go from there in these types of questions?

    The general form is y=C1e^-2x+C2e^5x

    Do I plug in x=0? That would leave C1+C2=10 which doesn't seem right....

    I need to get to y(x)=__________
    according to your question, you have y =1 , when x=0

    that gives you c1+c2=1

    and you also have y'=10 when x=0

    so find the derivative of y={C_1}e^{-2x}+{C_2}e^{5x}, and use y'(0) = 10 and you will get c1+c2=(some number)..

    so you will have 2 equations from which you can find out c1 and c2 and complete your equation for y
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