Question

Differential Equation.

Answer 1

\[\frac{ dr }{ d \theta } +rtan(\theta)=\sec(\theta)\]

Answer 2

Integrating factor
\[e^{\int\limits_{}^{}\tan(\theta) d \theta }=-\cos(\theta)\]

Answer 3

Or is it done by switched over the tan(theta) towards the right side and finding an identity?

Answer 4

\[\frac{ dr }{ d \theta } = \sec(\theta) - rtan(\theta)\]
Removing a sec(theta) we arrive at
\[\frac{ dr }{ d \theta }= \sec(\theta)(1-\sin(\theta))\]

Answer 5

Missing an r so i really meant:
\[\frac{ dr }{ d \theta } = \sec(\theta)(1-rsin(\theta))\]

Answer 6

look at your integrating factor again

Answer 7

It would end up as:
\[-\cos(\theta) r = -\theta+c\]

Answer 8

so
\[r = \frac{ \theta }{ \cos(\theta) }+\frac{ c }{ \cos(\theta) }\]

Answer 9

or 1/cos(theta) = sec(theta)
r = sec(Theta)theta+sec(theta)C
r = sec(theta)(theta+c)

Answer 10

Doesn't seem quite right

Answer 11

your integrating factor is not correct

Answer 12

DId you mean the integrating factor would be cos^-1?

Answer 13

I've thought of that as well

Answer 14

correct ..it is the sec(theta)

Answer 15

\[\sec(\theta)r=-\theta+c\]?

Answer 16

\[\sec(\theta)\frac{ dr }{ d \theta } +r\sec(\theta)\tan(\theta)=\sec^2(\theta)\]

Answer 17

\[\frac{ 1 }{ \cos(\theta)}\frac{ dr }{ d \theta }+rsec(\theta)\tan(\theta)= \sec^2(\theta)\]

Answer 18

\[\Large\frac{d}{d\theta}[r\sec(\theta)]=\sec^2(\theta)\]

Answer 19

then integrate

Answer 20

Ohh alright thank you very much

Answer 21

Simple little mistake with the integrating factor messed it all up

Answer 22

usually does