Question

Solve the differential equation.

Answer 1

\[\frac{ dy }{ dx } = \frac{ 1 }{ x \cos y + \sin 2y }\]

Answer 2

i smell the stench of that "uv sub" thingy

Answer 3

Guess so.

Answer 4

Well... You know the identity got sin (2y) at least.

Answer 5

Tried solving it... I am unable to separate the x and the y.

Answer 6

Yeah,same problem. Not understanding what method to use.

Answer 7

A stupid idea:
\[\frac{ dy }{ dx } = \frac{ 1 }{ x \cos y + \sin 2y }\]\[\frac{ dx }{ dy } = x \cos y + \sin 2y\]Solve this and you get x = (something in y), then change y into the subject.

Answer 8

Got the idea finally,
Invert it first,\[\frac{ dx }{ dy } = x \cos y + \sin 2y \]
Now use the concept of linear equation. But interchanging y and x.
\[\frac{ dx }{dy } +x P(y) = Q(y)\]
Use integrating factor,\[e ^{\int\limits_{}^{}P(y)dy}\]

Answer 9

@Callisto , not a stupid idea. :)

Answer 10

Wow never even thought of that...