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Math Help - simple ODE

  1. #1
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    simple ODE

    I'm taking a first course in DE. Is this problem in the form \frac{dy}{dt}+ay=g(t)? How do I solve it?

    y\prime + 3y = t + e^{-2t}
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Hoover glasses View Post
    I'm taking a first course in DE. Is this problem in the form \frac{dy}{dt}+ay=g(t)? How do I solve it?

    y\prime + 3y = t + e^{-2t}
    y' + ay = g(t) .........................multiply through by e^{at}

    \Rightarrow e^{at}y' + ae^{at}y = e^{at}g(t) .........simplify the left hand side

    \Rightarrow (e^{at}y)' = e^{at}g(t) ..................integrate both sides

    \Rightarrow e^{at}y = \int e^{at}g(t)~dt .............solve for y

    \Rightarrow y = \frac {\int e^{at}g(t)~dt}{e^{at}}
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  3. #3
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    I get

    y = \frac{t}{3} -1/9 +e^{-2t} + ce^{-3t}
    Last edited by Hoover glasses; September 17th 2008 at 02:08 AM. Reason: oops
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