[2x+ycos(xy)]dx+[xcos(xy)-2y]dy=0

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Solution for [2x+ycos(xy)]dx+[xcos(xy)-2y]dy=0 equation: 


Simplifying
[2x + ycos(xy)] * dx + [xcos(xy) + -2y] * dy = 0

Multiply cosy * xy
[2x + cosxy2] * dx + [xcos(xy) + -2y] * dy = 0

Reorder the terms:
[cosxy2 + 2x] * dx + [xcos(xy) + -2y] * dy = 0

Reorder the terms for easier multiplication:
dx[cosxy2 + 2x] + [xcos(xy) + -2y] * dy = 0
[cosxy2 * dx + 2x * dx] + [xcos(xy) + -2y] * dy = 0
[cdosx2y2 + 2dx2] + [xcos(xy) + -2y] * dy = 0

Multiply cosx * xy
cdosx2y2 + 2dx2 + [cosx2y + -2y] * dy = 0

Reorder the terms for easier multiplication:
cdosx2y2 + 2dx2 + dy[cosx2y + -2y] = 0
cdosx2y2 + 2dx2 + [cosx2y * dy + -2y * dy] = 0
cdosx2y2 + 2dx2 + [cdosx2y2 + -2dy2] = 0

Reorder the terms:
cdosx2y2 + cdosx2y2 + 2dx2 + -2dy2 = 0

Combine like terms: cdosx2y2 + cdosx2y2 = 2cdosx2y2
2cdosx2y2 + 2dx2 + -2dy2 = 0

Solving
2cdosx2y2 + 2dx2 + -2dy2 = 0

Solving for variable 'c'.

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

Add '-2dx2' to each side of the equation.
2cdosx2y2 + 2dx2 + -2dx2 + -2dy2 = 0 + -2dx2

Combine like terms: 2dx2 + -2dx2 = 0
2cdosx2y2 + 0 + -2dy2 = 0 + -2dx2
2cdosx2y2 + -2dy2 = 0 + -2dx2
Remove the zero:
2cdosx2y2 + -2dy2 = -2dx2

Add '2dy2' to each side of the equation.
2cdosx2y2 + -2dy2 + 2dy2 = -2dx2 + 2dy2

Combine like terms: -2dy2 + 2dy2 = 0
2cdosx2y2 + 0 = -2dx2 + 2dy2
2cdosx2y2 = -2dx2 + 2dy2

Divide each side by '2dosx2y2'.
c = -1o-1s-1y-2 + o-1s-1x-2

Simplifying
c = -1o-1s-1y-2 + o-1s-1x-2

Reorder the terms:
c = o-1s-1x-2 + -1o-1s-1y-2

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