(x*sin(y)+y*cos(y))dx+(x*cos(y)-y*sin(y))dy=0

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Solution for (x*sin(y)+y*cos(y))dx+(x*cos(y)-y*sin(y))dy=0 equation: 


Simplifying
(x * sin(y) + y * cos(y)) * dx + (x * cos(y) + -1y * sin(y)) * dy = 0

Multiply x * ins
(insx * y + y * cos(y)) * dx + (x * cos(y) + -1y * sin(y)) * dy = 0

Multiply insx * y
(insxy + y * cos(y)) * dx + (x * cos(y) + -1y * sin(y)) * dy = 0

Multiply y * cos
(insxy + cosy * y) * dx + (x * cos(y) + -1y * sin(y)) * dy = 0

Multiply cosy * y
(insxy + cosy2) * dx + (x * cos(y) + -1y * sin(y)) * dy = 0

Reorder the terms:
(cosy2 + insxy) * dx + (x * cos(y) + -1y * sin(y)) * dy = 0

Reorder the terms for easier multiplication:
dx(cosy2 + insxy) + (x * cos(y) + -1y * sin(y)) * dy = 0
(cosy2 * dx + insxy * dx) + (x * cos(y) + -1y * sin(y)) * dy = 0
(cdosxy2 + dinsx2y) + (x * cos(y) + -1y * sin(y)) * dy = 0

Multiply x * cos
cdosxy2 + dinsx2y + (cosx * y + -1y * sin(y)) * dy = 0

Multiply cosx * y
cdosxy2 + dinsx2y + (cosxy + -1y * sin(y)) * dy = 0

Multiply y * ins
cdosxy2 + dinsx2y + (cosxy + -1insy * y) * dy = 0

Multiply insy * y
cdosxy2 + dinsx2y + (cosxy + -1insy2) * dy = 0

Reorder the terms for easier multiplication:
cdosxy2 + dinsx2y + dy(cosxy + -1insy2) = 0
cdosxy2 + dinsx2y + (cosxy * dy + -1insy2 * dy) = 0
cdosxy2 + dinsx2y + (cdosxy2 + -1dinsy3) = 0

Reorder the terms:
cdosxy2 + cdosxy2 + dinsx2y + -1dinsy3 = 0

Combine like terms: cdosxy2 + cdosxy2 = 2cdosxy2
2cdosxy2 + dinsx2y + -1dinsy3 = 0

Solving
2cdosxy2 + dinsx2y + -1dinsy3 = 0

Solving for variable 'c'.

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

Add '-1dinsx2y' to each side of the equation.
2cdosxy2 + dinsx2y + -1dinsx2y + -1dinsy3 = 0 + -1dinsx2y

Combine like terms: dinsx2y + -1dinsx2y = 0
2cdosxy2 + 0 + -1dinsy3 = 0 + -1dinsx2y
2cdosxy2 + -1dinsy3 = 0 + -1dinsx2y
Remove the zero:
2cdosxy2 + -1dinsy3 = -1dinsx2y

Add 'dinsy3' to each side of the equation.
2cdosxy2 + -1dinsy3 + dinsy3 = -1dinsx2y + dinsy3

Combine like terms: -1dinsy3 + dinsy3 = 0
2cdosxy2 + 0 = -1dinsx2y + dinsy3
2cdosxy2 = -1dinsx2y + dinsy3

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

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

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

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