2*cos(2x-y)dx-cos(2x-y)dy=0

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


Simplifying
2cos(2x + -1y) * dx + -1cos(2x + -1y) * dy = 0

Reorder the terms for easier multiplication:
2cos * dx(2x + -1y) + -1cos(2x + -1y) * dy = 0

Multiply cos * dx
2cdosx(2x + -1y) + -1cos(2x + -1y) * dy = 0
(2x * 2cdosx + -1y * 2cdosx) + -1cos(2x + -1y) * dy = 0

Reorder the terms:
(-2cdosxy + 4cdosx2) + -1cos(2x + -1y) * dy = 0
(-2cdosxy + 4cdosx2) + -1cos(2x + -1y) * dy = 0

Reorder the terms for easier multiplication:
-2cdosxy + 4cdosx2 + -1cos * dy(2x + -1y) = 0

Multiply cos * dy
-2cdosxy + 4cdosx2 + -1cdosy(2x + -1y) = 0
-2cdosxy + 4cdosx2 + (2x * -1cdosy + -1y * -1cdosy) = 0
-2cdosxy + 4cdosx2 + (-2cdosxy + 1cdosy2) = 0

Reorder the terms:
-2cdosxy + -2cdosxy + 4cdosx2 + 1cdosy2 = 0

Combine like terms: -2cdosxy + -2cdosxy = -4cdosxy
-4cdosxy + 4cdosx2 + 1cdosy2 = 0

Solving
-4cdosxy + 4cdosx2 + 1cdosy2 = 0

Solving for variable 'c'.

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

Factor out the Greatest Common Factor (GCF), 'cdos'.
cdos(-4xy + 4x2 + y2) = 0

Factor a trinomial.
cdos((2x + -1y)(2x + -1y)) = 0

Subproblem 1

Set the factor 'cdos' equal to zero and attempt to solve: Simplifying cdos = 0 Solving cdos = 0 Move all terms containing c to the left, all other terms to the right. Simplifying cdos = 0 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 '(2x + -1y)' equal to zero and attempt to solve: Simplifying 2x + -1y = 0 Solving 2x + -1y = 0 Move all terms containing c to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + -2x + -1y = 0 + -2x Combine like terms: 2x + -2x = 0 0 + -1y = 0 + -2x -1y = 0 + -2x Remove the zero: -1y = -2x Add 'y' to each side of the equation. -1y + y = -2x + y Combine like terms: -1y + y = 0 0 = -2x + y Simplifying 0 = -2x + y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(2x + -1y)' equal to zero and attempt to solve: Simplifying 2x + -1y = 0 Solving 2x + -1y = 0 Move all terms containing c to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + -2x + -1y = 0 + -2x Combine like terms: 2x + -2x = 0 0 + -1y = 0 + -2x -1y = 0 + -2x Remove the zero: -1y = -2x Add 'y' to each side of the equation. -1y + y = -2x + y Combine like terms: -1y + y = 0 0 = -2x + y Simplifying 0 = -2x + y 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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