(x+siny)dx+(xcosy+siny)dy=0

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Solution for (x+siny)dx+(xcosy+siny)dy=0 equation: 


Simplifying
(x + siny) * dx + (xcosy + siny) * dy = 0

Reorder the terms:
(insy + x) * dx + (xcosy + siny) * dy = 0

Reorder the terms for easier multiplication:
dx(insy + x) + (xcosy + siny) * dy = 0
(insy * dx + x * dx) + (xcosy + siny) * dy = 0
(dinsxy + dx2) + (xcosy + siny) * dy = 0

Reorder the terms for easier multiplication:
dinsxy + dx2 + dy(cosxy + insy) = 0
dinsxy + dx2 + (cosxy * dy + insy * dy) = 0
dinsxy + dx2 + (cdosxy2 + dinsy2) = 0

Reorder the terms:
cdosxy2 + dinsxy + dinsy2 + dx2 = 0

Solving
cdosxy2 + dinsxy + dinsy2 + dx2 = 0

Solving for variable 'c'.

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

Add '-1dinsxy' to each side of the equation.
cdosxy2 + dinsxy + dinsy2 + -1dinsxy + dx2 = 0 + -1dinsxy

Reorder the terms:
cdosxy2 + dinsxy + -1dinsxy + dinsy2 + dx2 = 0 + -1dinsxy

Combine like terms: dinsxy + -1dinsxy = 0
cdosxy2 + 0 + dinsy2 + dx2 = 0 + -1dinsxy
cdosxy2 + dinsy2 + dx2 = 0 + -1dinsxy
Remove the zero:
cdosxy2 + dinsy2 + dx2 = -1dinsxy

Add '-1dinsy2' to each side of the equation.
cdosxy2 + dinsy2 + -1dinsy2 + dx2 = -1dinsxy + -1dinsy2

Combine like terms: dinsy2 + -1dinsy2 = 0
cdosxy2 + 0 + dx2 = -1dinsxy + -1dinsy2
cdosxy2 + dx2 = -1dinsxy + -1dinsy2

Add '-1dx2' to each side of the equation.
cdosxy2 + dx2 + -1dx2 = -1dinsxy + -1dinsy2 + -1dx2

Combine like terms: dx2 + -1dx2 = 0
cdosxy2 + 0 = -1dinsxy + -1dinsy2 + -1dx2
cdosxy2 = -1dinsxy + -1dinsy2 + -1dx2

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

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

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

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