Question

Differential equations. sin (theta)(dr/dtheta)+(costheta)r= tantheta, 0 12 years ago

Answer 1

this is my work so far

Answer 2

but I can't find the answer for r

Answer 3

I don't see anything wrong with your work. If there's no initial condition given, then the general solution is simply \(r(\theta)=\csc\theta(c+\ln(\sec\theta))\). If there was an initial condition \(r(\theta_0)=r_0\), then \(c=r_0\sin\theta_0+\ln(\cos\theta_0)\) (as you have already determined) and thus \(r(\theta)=\csc\theta(r_0\sin\theta_0 + \ln(\cos\theta_0\cdot\sec\theta))\) would be your solution.

The restriction \(0<\theta<\pi/2\) is necessary in order to guarantee that the \(r(\theta)\) we found exists.

Does this clarify things?