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

[ckp]

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 can't solve.

this is my work. hope it doesn't 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.

 

[rock.freak667]

$$\frac{dr}{d \theta} + r sec\theta=cos\theta$$


looks a bit like

$$\frac{dy}{dx} + yP(x)=Q(x)$$

doesn't it? So try an integrating factor.

 

[ckp]

i was trying to use an integrating factor, but I am not sure if I am using it right. the long mess is what i end up with and i can't go any further. my book doesn't do a very good job of explaining it

 

[ckp]

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

got it now.