how to find the general solution of this:
cos y sin 2x dx + ( (cos y)^2 -(cos x )^2)dy = 0

I am trying substitution but I can't find anything that will lead me to a solution

Question

how to find the general solution of this:
cos y sin 2x dx + ( (cos y)^2 -(cos x )^2)dy = 0

I am trying substitution but I can't find anything that will lead me to a solution

moongazer · Answer

@UnkleRhaukus

unklerhaukus · Answer

If
      M  = cos y sin 2x      &      N =  (cos y)^2 -(cos x )^2

What are 
     M_y  =                       &       N_x = 
?

moongazer · Answer

what does M_y,  N_x mean? I am not familiar with that notation.

unklerhaukus · Answer

M_y = $M_y= \dfrac{\partial M}{\partial y}$ =  partial derivative of M with respect to y

moongazer · Answer

ok thanks

unklerhaukus · Answer

do you know how to take partial derivatives?

moongazer · Answer

yes, i'll just solve it. brb :)

moongazer · Answer

M_y =-sin y sin 2x
N_x = 2sin x cos x  = sin 2x 

am I right ?

unklerhaukus · Answer

hmm , yeah,

moongazer · Answer

I think I can use determination of integrating factors here.

unklerhaukus · Answer

i thought they were going to be equal ,

unklerhaukus · Answer

i'm not sure how to solve this DE

moongazer · Answer

I think i'm getting near to the solution.

moongazer · Answer

I got it!. I used  determination of integrating factors. Thanks for the spark!. I got the idea when you made me test the exactness. :)

unklerhaukus · Answer

you got it! well done , can i see how you did it?