(x*cosy-y*seny)dy+(x*seny+y*cosy)dx=0

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Solution for (x*cosy-y*seny)dy+(x*seny+y*cosy)dx=0 equation: 


Simplifying
(x * cosy + -1y * seny) * dy + (x * seny + y * cosy) * dx = 0

Multiply x * cosy
(cosxy + -1y * seny) * dy + (x * seny + y * cosy) * dx = 0

Multiply y * ensy
(cosxy + -1ensy2) * dy + (x * seny + y * cosy) * dx = 0

Reorder the terms for easier multiplication:
dy(cosxy + -1ensy2) + (x * seny + y * cosy) * dx = 0
(cosxy * dy + -1ensy2 * dy) + (x * seny + y * cosy) * dx = 0
(cdosxy2 + -1densy3) + (x * seny + y * cosy) * dx = 0

Multiply x * ensy
cdosxy2 + -1densy3 + (ensxy + y * cosy) * dx = 0

Multiply y * cosy
cdosxy2 + -1densy3 + (ensxy + cosy2) * dx = 0

Reorder the terms:
cdosxy2 + -1densy3 + (cosy2 + ensxy) * dx = 0

Reorder the terms for easier multiplication:
cdosxy2 + -1densy3 + dx(cosy2 + ensxy) = 0
cdosxy2 + -1densy3 + (cosy2 * dx + ensxy * dx) = 0
cdosxy2 + -1densy3 + (cdosxy2 + densx2y) = 0

Reorder the terms:
cdosxy2 + cdosxy2 + densx2y + -1densy3 = 0

Combine like terms: cdosxy2 + cdosxy2 = 2cdosxy2
2cdosxy2 + densx2y + -1densy3 = 0

Solving
2cdosxy2 + densx2y + -1densy3 = 0

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '-1densx2y' to each side of the equation.
2cdosxy2 + densx2y + -1densx2y + -1densy3 = 0 + -1densx2y

Combine like terms: densx2y + -1densx2y = 0
2cdosxy2 + 0 + -1densy3 = 0 + -1densx2y
2cdosxy2 + -1densy3 = 0 + -1densx2y
Remove the zero:
2cdosxy2 + -1densy3 = -1densx2y

Add 'densy3' to each side of the equation.
2cdosxy2 + -1densy3 + densy3 = -1densx2y + densy3

Combine like terms: -1densy3 + densy3 = 0
2cdosxy2 + 0 = -1densx2y + densy3
2cdosxy2 = -1densx2y + densy3

Divide each side by '2dosxy2'.
c = -0.5eno-1xy-1 + 0.5eno-1x-1y

Simplifying
c = -0.5eno-1xy-1 + 0.5eno-1x-1y

Reorder the terms:
c = 0.5eno-1x-1y + -0.5eno-1xy-1

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