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Math Help - Finding a solution given initial value problem

  1. #1
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    Finding a solution given initial value problem

    Code:
    y'-y=7te2t   , y(0)=1

    I would like to know how to solve this Differential Equation. I think I have to find the integrating factor.

    It does look like it follows the the standard form
    Code:
    y'+px=qx
    So the integrating factor is e∫px

    Would the integrating factor be e∫-y ?

    Thanks
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Finding a solution given initial value problem

    Your integrating factor would be:

    \mu(t)=e^{\int(-1)\,dt}=e^{-t}

    Multiplying the ODE by this factor will give you the product of differentiation on the left:

    e^{-t}\frac{dy}{dt}-e^{-t}y=7te^t

    \frac{d}{dt}\left(e^{-t}y \right)=7te^t

    \int\,d\left(e^{-t}y \right)=7\int te^t\,dt

    Now, use integration by parts on the right...
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  3. #3
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    Re: Finding a solution given initial value problem

    How do you insert mathematical functions on these forums the way you inserted the integral sign?

    And thanks for the integrating factor.
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Finding a solution given initial value problem

    Use the TEX tags, for example enclosing the code \int_a^b f(x)\,dx=F(b)-F(a) within the tags produces:

    \int_a^b f(x)\,dx=F(b)-F(a)
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