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Math Help - Help for a friend

  1. #1
    Member eXist's Avatar
    Joined
    Aug 2009
    Posts
    157

    Help for a friend

    My friend came to me with a problem from his differential equations class, and unfortunately I don't understand the directions. This is all he gave me, any help is much appreciated:

    By substitution, determine the correct solution to the differential equation:

    y' = y + 13e^{-x}

    I can integrate and solve for y by completing the square but I'm not sure that's correct.
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  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
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    Florida
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    Re write

    y ' - y = 13e^(-x)

    multiply both sides by e^(-x)

    e^(-x)y ' -e^(-x) y =13 e^(-2x)

    Note the LHS is

    d(e^(-x)y)/dx = 13e^(-2x)

    Integrate

    e^(-x)y = -13/2 e^(-2x) + C

    y = -13/2 e^(-x) + C e^(x)
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