(Y+xy+siny)dx+(xcosy)dy=0

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


Simplifying
(Y + xy + siny) * dx + (xcosy) * dy = 0

Reorder the terms:
(Y + insy + xy) * dx + (xcosy) * dy = 0

Reorder the terms for easier multiplication:
dx(Y + insy + xy) + (xcosy) * dy = 0
(Y * dx + insy * dx + xy * dx) + (xcosy) * dy = 0

Reorder the terms:
(dinsxy + dxY + dx2y) + (xcosy) * dy = 0
(dinsxy + dxY + dx2y) + (xcosy) * dy = 0

Multiply cosxy * dy
dinsxy + dxY + dx2y + cdosxy2 = 0

Reorder the terms:
cdosxy2 + dinsxy + dxY + dx2y = 0

Solving
cdosxy2 + dinsxy + dxY + dx2y = 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 + dxY + -1dinsxy + dx2y = 0 + -1dinsxy

Reorder the terms:
cdosxy2 + dinsxy + -1dinsxy + dxY + dx2y = 0 + -1dinsxy

Combine like terms: dinsxy + -1dinsxy = 0
cdosxy2 + 0 + dxY + dx2y = 0 + -1dinsxy
cdosxy2 + dxY + dx2y = 0 + -1dinsxy
Remove the zero:
cdosxy2 + dxY + dx2y = -1dinsxy

Add '-1dxY' to each side of the equation.
cdosxy2 + dxY + -1dxY + dx2y = -1dinsxy + -1dxY

Combine like terms: dxY + -1dxY = 0
cdosxy2 + 0 + dx2y = -1dinsxy + -1dxY
cdosxy2 + dx2y = -1dinsxy + -1dxY

Add '-1dx2y' to each side of the equation.
cdosxy2 + dx2y + -1dx2y = -1dinsxy + -1dxY + -1dx2y

Combine like terms: dx2y + -1dx2y = 0
cdosxy2 + 0 = -1dinsxy + -1dxY + -1dx2y
cdosxy2 = -1dinsxy + -1dxY + -1dx2y

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

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

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

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