Elementary differential equations: Linear equations

  • Thread starter Mdhiggenz
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  • #1
Mdhiggenz
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Homework Statement



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?

Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
LCKurtz
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Homework Statement



dr/d∅+rtan∅=cos∅

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

##e^{-\ln\cos\phi}=e^{\ln[(cos\phi)^{-1}]} =\frac 1 {\cos\phi}##
 
  • #3
Mdhiggenz
327
1
Thanks LC!
 

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