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Thread: differential equation working

  1. #1
    Nov 2010

    differential equation working

    Hello, I am looking at the differential equation:
    dR/DΘ + R = e^-Θ * sec^2Θ

    I understand how to use e^(integral of e^(1dΘ) to multiply both sides which gives me:

    (looking at left hand side of equation only)
    e^Θ * dR/dΘ + e^Θ * R

    However I am not sure how to further simplify the left hand side of the equation before integrating.
    Can someone please show me the process for doing that.

    Thanks kindly for any help.
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  2. #2
    Senior Member BAdhi's Avatar
    Oct 2010
    Gampaha, Sri Lanka

    Re: differential equation working

    now you can use the property -

    $\displaystyle \frac{du}{d\theta}v+\frac{dv}{d\theta}u=\frac{duv} {d\theta}$

    where $\displaystyle u=e^\theta$ and $\displaystyle v=R$

    eventually you'll get

    $\displaystyle \frac{d(e^\theta R)}{d\theta}=\sec^2\theta$
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