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Elementary differential equations: Linear equations

  1. Sep 16, 2012 #1
    1. The problem statement, all variables and given/known data

    dr/d∅+rtan∅=cos∅

    μ(∅)=exp[∫tan∅]
    μ∅=exp[-ln[cos∅]=-cos∅

    -cos∅(dr/d∅)-rtan∅cos∅=-cos^2∅
    dr/d∅[-rcos∅]=-cos^2∅

    rcos∅=∫cos^2∅

    changed cos^2∅ to 1/2+1/2cos2∅
    rcos∅=1/2∅ + 1/4 sin2∅+c

    the books answer is not even close to mine they have r=(∅+c)cos∅

    Where did I go wrong?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 16, 2012 #2

    LCKurtz

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    ##e^{-\ln\cos\phi}=e^{\ln[(cos\phi)^{-1}]} =\frac 1 {\cos\phi}##
     
  4. Sep 16, 2012 #3
    Thanks LC!
     
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