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General solution of DE

  1. Sep 10, 2009 #1

    ckp

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    dr/d(theta) + r*sec(theta) = cos(theta)

    apparently the solution is (sec(theta) + tan(theta))*r = theta - cos(theta) + c

    but i have no idea how to get there.

    i am using a technique from the book, but it yeilds an answer with lots of e's and an integral i cant solve.

    this is my work. hope it doesnt look like a complete mess

    ce^(-(sec(theta)tan(theta))) + e^(-(sec(theta)tan(theta)))(integral([e^(sec(theta)tan(theta))]cos(theta))d(theta)]

    and i have no idea what to do from here.
     
  2. jcsd
  3. Sep 10, 2009 #2

    rock.freak667

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    Homework Helper

    [tex]\frac{dr}{d \theta} + r sec\theta=cos\theta[/tex]


    looks a bit like

    [tex]\frac{dy}{dx} + yP(x)=Q(x)[/tex]

    doesn't it? So try an integrating factor.
     
  4. Sep 10, 2009 #3

    ckp

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    i was trying to use an integrating factor, but im not sure if im using it right. the long mess is what i end up with and i cant go any further. my book doesnt do a very good job of explaining it
     
  5. Sep 10, 2009 #4

    ckp

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    ha, nevermind. I'm sorry, I messed up the integral of sec(X) >_>

    got it now.
     
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