Integrating factor

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  1. music lover's Avatar
    1 03-08-2012  16:40
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    Integrating factor
    bit stuck on following a few steps of this: Consider dy/dx +Fy=G where F and G are both functions of x only. multiplying by I, a function of x then

    (I)(\frac{dy}{dx})+(y)(FI)= GI

    comparing LHS with x\frac{du}{dx}+u\frac{dv}{dx}

    we get v=I \frac{du}{dx}=\frac{dy}{dx}
    u=y \frac{dv}{dx}=FI. This implies that \frac{dI}{dx}=FI.

    I'm a bit unsure how get from dv/dx=FI to dI/dx=FI.
  2. steve10's Avatar
    2 03-08-2012  18:50
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    Re: Integrating factor
    You already had v=I (your 3rd line of working) from which \frac{dv}{dx}=\frac{dI}{dx}

    and \frac{dv}{dx}=FI (your 4th line of working) which implies \frac{dI}{dx}=FI.
  3. music lover's Avatar
    3 03-08-2012  18:51
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    • Posts: 146
    Re: Integrating factor
    (Original post by steve10)
    You already had v=I (your 3rd line of working) from which \frac{dv}{dx}=\frac{dI}{dx}

    and \frac{dv}{dx}=FI (your 4th line of working) which implies \frac{dI}{dx}=FI.
    Oh yeah, nice fail XD. Thank you .
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