Question

Find the general solution:

\[(r + \sin \theta - \cos \theta)dr + r(\sin \theta + \cos \theta)d\theta = 0\]

Answer 1

is this exact?

Answer 2

\[\frac{\partial M}{\partial \theta} = \cos \theta + \sin \theta\]
\[\frac{\partial N}{\partial r} = \sin \theta + \cos \theta\]
hmm it's exact...so i guess onto integration

Answer 3

\[\frac{r^2}{2} + r\sin \theta - r\cos \theta + g(y)\]

Answer 4

that's g(theta)

Answer 5

\[r\cos \theta + r\sin \theta + g'(y) = r\sin \theta + r\cos \theta\]
\[g(y) = 0\]
so G.S>
\[\frac{r^2}{2} + r\sin \theta - r\cos \theta= C\]
correct?

Answer 6

Yeah it is correct.

Answer 7

nice thanks