Question

Determine whether the given equation is separable, linear, neither, or both: dr/dtheta + rtan(theta) = sec(theta).

Answer 1

\(\sf \color{red}{\theta~'+r~tan(\theta)=sec(\theta)}\) is that correct?

Answer 2

You should recognize that this is a 1\(^{st}\) order linear differential equation.

Answer 3

Yes that's correct

Answer 4

I set x = r and y = \[\theta \] and I got dy/dx = sec(y) - xtan(y)

Answer 5

Why are you changing the variables?

Answer 6

To make it a little easier

Answer 7

Hmm, if it helps you then by all means. But what are you doing now? Solving?

Answer 8

I'm trying that's why I post the question

Answer 9

Well, you should of left it like it was before. You need to start by finding the integrating factor, \(\sf \color{red}{\mu(x)}\). Can you do that?

Answer 10

You mean μ(r) since I should not have change it. If so, μ(r) = e^(r^2/2).

Answer 11

Well, I just changed it to \(x\) since you changed it, but you're actually integrating \(\sf \color{purple}{tan(\theta)~d\theta}\)

Answer 12

I thought the r would be considered p(x) and the tan(theta) = q(x) hence, μ(x) = the integral of p(x)

Answer 13

Well, continue with what you're doing and we will see the answer you get.

Answer 14

I will work on it with you.