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

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


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

Reorder the terms for easier multiplication:
dx(cosx + ensy) + (senx + cosy) * dy = 0
(cosx * dx + ensy * dx) + (senx + cosy) * dy = 0
(cdosx2 + densxy) + (senx + cosy) * dy = 0

Reorder the terms:
cdosx2 + densxy + (cosy + ensx) * dy = 0

Reorder the terms for easier multiplication:
cdosx2 + densxy + dy(cosy + ensx) = 0
cdosx2 + densxy + (cosy * dy + ensx * dy) = 0
cdosx2 + densxy + (cdosy2 + densxy) = 0

Reorder the terms:
cdosx2 + cdosy2 + densxy + densxy = 0

Combine like terms: densxy + densxy = 2densxy
cdosx2 + cdosy2 + 2densxy = 0

Solving
cdosx2 + cdosy2 + 2densxy = 0

Solving for variable 'c'.

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

Add '-2densxy' to each side of the equation.
cdosx2 + cdosy2 + 2densxy + -2densxy = 0 + -2densxy

Combine like terms: 2densxy + -2densxy = 0
cdosx2 + cdosy2 + 0 = 0 + -2densxy
cdosx2 + cdosy2 = 0 + -2densxy
Remove the zero:
cdosx2 + cdosy2 = -2densxy

Combine like terms: -2densxy + 2densxy = 0
cdosx2 + cdosy2 + 2densxy = 0

Factor out the Greatest Common Factor (GCF), 'ds'.
ds(cox2 + coy2 + 2enxy) = 0


Subproblem 1
Set the factor 'ds' equal to zero and attempt to solve:

Simplifying
ds = 0

Solving
ds = 0

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

Add '-1ds' to each side of the equation.
ds + -1ds = 0 + -1ds
Remove the zero:
0 = -1ds

Simplifying
0 = -1ds

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(cox2 + coy2 + 2enxy)' equal to zero and attempt to solve:

Simplifying
cox2 + coy2 + 2enxy = 0

Solving
cox2 + coy2 + 2enxy = 0

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

Add '-2enxy' to each side of the equation.
cox2 + coy2 + 2enxy + -2enxy = 0 + -2enxy

Combine like terms: 2enxy + -2enxy = 0
cox2 + coy2 + 0 = 0 + -2enxy
cox2 + coy2 = 0 + -2enxy
Remove the zero:
cox2 + coy2 = -2enxy

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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