(x+senx+seny)dx+(cosy)dy=0

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Solution for (x+senx+seny)dx+(cosy)dy=0 equation:


Simplifying
(x + senx + seny) * dx + (cosy) * dy = 0

Reorder the terms:
(ensx + ensy + x) * dx + (cosy) * dy = 0

Reorder the terms for easier multiplication:
dx(ensx + ensy + x) + (cosy) * dy = 0
(ensx * dx + ensy * dx + x * dx) + (cosy) * dy = 0

Reorder the terms:
(densxy + densx2 + dx2) + (cosy) * dy = 0
(densxy + densx2 + dx2) + (cosy) * dy = 0

Multiply cosy * dy
densxy + densx2 + dx2 + cdosy2 = 0

Reorder the terms:
cdosy2 + densxy + densx2 + dx2 = 0

Solving
cdosy2 + densxy + densx2 + dx2 = 0

Solving for variable 'c'.

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

Add '-1densxy' to each side of the equation.
cdosy2 + densxy + densx2 + -1densxy + dx2 = 0 + -1densxy

Reorder the terms:
cdosy2 + densxy + -1densxy + densx2 + dx2 = 0 + -1densxy

Combine like terms: densxy + -1densxy = 0
cdosy2 + 0 + densx2 + dx2 = 0 + -1densxy
cdosy2 + densx2 + dx2 = 0 + -1densxy
Remove the zero:
cdosy2 + densx2 + dx2 = -1densxy

Add '-1densx2' to each side of the equation.
cdosy2 + densx2 + -1densx2 + dx2 = -1densxy + -1densx2

Combine like terms: densx2 + -1densx2 = 0
cdosy2 + 0 + dx2 = -1densxy + -1densx2
cdosy2 + dx2 = -1densxy + -1densx2

Add '-1dx2' to each side of the equation.
cdosy2 + dx2 + -1dx2 = -1densxy + -1densx2 + -1dx2

Combine like terms: dx2 + -1dx2 = 0
cdosy2 + 0 = -1densxy + -1densx2 + -1dx2
cdosy2 = -1densxy + -1densx2 + -1dx2

Divide each side by 'dosy2'.
c = -1eno-1xy-1 + -1eno-1x2y-2 + -1o-1s-1x2y-2

Simplifying
c = -1eno-1xy-1 + -1eno-1x2y-2 + -1o-1s-1x2y-2

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