(y-cos^2(x))dx+cos(x)dy=0

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Solution for (y-cos^2(x))dx+cos(x)dy=0 equation: 


Simplifying
(y + -1cos2(x)) * dx + cos(x) * dy = 0

Multiply cos2 * x
(y + -1cos2x) * dx + cos(x) * dy = 0

Reorder the terms:
(-1cos2x + y) * dx + cos(x) * dy = 0

Reorder the terms for easier multiplication:
dx(-1cos2x + y) + cos(x) * dy = 0
(-1cos2x * dx + y * dx) + cos(x) * dy = 0
(-1cdos2x2 + dxy) + cos(x) * dy = 0

Multiply cos * x
-1cdos2x2 + dxy + cosx * dy = 0

Multiply cosx * dy
-1cdos2x2 + dxy + cdosxy = 0

Reorder the terms:
cdosxy + -1cdos2x2 + dxy = 0

Solving
cdosxy + -1cdos2x2 + dxy = 0

Solving for variable 'c'.

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

Add '-1dxy' to each side of the equation.
cdosxy + -1cdos2x2 + dxy + -1dxy = 0 + -1dxy

Combine like terms: dxy + -1dxy = 0
cdosxy + -1cdos2x2 + 0 = 0 + -1dxy
cdosxy + -1cdos2x2 = 0 + -1dxy
Remove the zero:
cdosxy + -1cdos2x2 = -1dxy

Combine like terms: -1dxy + dxy = 0
cdosxy + -1cdos2x2 + dxy = 0

Factor out the Greatest Common Factor (GCF), 'dx'.
dx(cosy + -1cos2x + y) = 0


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

Simplifying
dx = 0

Solving
dx = 0

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

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

Simplifying
0 = -1dx

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 '(cosy + -1cos2x + y)' equal to zero and attempt to solve:

Simplifying
cosy + -1cos2x + y = 0

Solving
cosy + -1cos2x + y = 0

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

Add '-1y' to each side of the equation.
cosy + -1cos2x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
cosy + -1cos2x + 0 = 0 + -1y
cosy + -1cos2x = 0 + -1y
Remove the zero:
cosy + -1cos2x = -1y

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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