Originally Posted by

**DistantCube** Okay here's the problem, I can't seem to find an integrating factor for this differential equation. As the original equation doesn't come out to be exact, we need an integrating factor to make it exact then we can solve it as an exact DE.

The equation is;

[sin(y)cos(y) + xcos^2(y)]dx + x.dy = 0 ---(1)

which is the same as;

[1/2sin(2y) + xcos^2(y)]dx + x.dy = 0

now if we let;

A = 1/2sin(2y) + xcos^2(y)

and

B = x

and take the partial derivatives of both;

dA/dy = cos(2y) - xsin(2y)

dB/dx = 1

and since dA/dy does not equal dB/dx we use either

i. (1/A)[dB/dx - dA/dy]

or

ii. (1/B)[dA/dy - dB/dx]

to get a function dependant **only** on y *or* **only** on x

...and I can't get that. I've tried various trig identities with no success, maybe I've messed up the basic differentiation there, or maybe I've missed an identity, I'm not sure. If someone can help me with the integrating factor, I'm fairly certain I can find the general solution to the equation easily.

.