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Math Help - find the value that satisfies intial conditions

  1. #1
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    find the value that satisfies intial conditions

    It is easy to check that for any value of c, the function

    y=ce^2x+e^x
    is solution of equation
    y+2y=e^x
    Find the value of c for which the solution satisfies the initial condition y(3)=4

    can someone solve this one?
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  2. #2
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    Quote Originally Posted by dat1611 View Post

    y+2y=e^x
    Are you sure you don't mean y'+2y=e^{x} ?

    Quote Originally Posted by dat1611 View Post

    y=ce^2x+e^x

    Find the value of c for which the solution satisfies the initial condition y(-3)=4
    y=ce^{-2x}+e^{-x}

    Using y(-3)=4

    4=ce^{-2\times -3}+e^{-(-3)}

    4=ce^{6}+e^{3}

    4-e^{3}=ce^{6}

    \frac{4-e^{3}}{e^{6}}=c

    c=\frac{4-e^{3}}{e^{6}}

    Therefore

    y=\left(\frac{4-e^{3}}{e^{6}}\right)e^{2x}+e^{x}
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