Elementary differential equations: Linear equations

[Mdhiggenz]

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

 

[LCKurtz]

Homework Statement

dr/d∅+rtan∅=cos∅

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

$e^{-\ln\cos\phi}=e^{\ln[(cos\phi)^{-1}]} =\frac 1 {\cos\phi}$

 

[Mdhiggenz]

Thanks LC!