(ycosx-siny)dx+(sinx-xcosy)dy=0

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Solution for (ycosx-siny)dx+(sinx-xcosy)dy=0 equation:


Simplifying
(ycosx + -1siny) * dx + (sinx + -1xcosy) * dy = 0

Reorder the terms for easier multiplication:
dx(cosxy + -1insy) + (sinx + -1xcosy) * dy = 0
(cosxy * dx + -1insy * dx) + (sinx + -1xcosy) * dy = 0
(cdosx2y + -1dinsxy) + (sinx + -1xcosy) * dy = 0

Reorder the terms:
cdosx2y + -1dinsxy + (-1cosxy + insx) * dy = 0

Reorder the terms for easier multiplication:
cdosx2y + -1dinsxy + dy(-1cosxy + insx) = 0
cdosx2y + -1dinsxy + (-1cosxy * dy + insx * dy) = 0
cdosx2y + -1dinsxy + (-1cdosxy2 + dinsxy) = 0

Reorder the terms:
-1cdosxy2 + cdosx2y + -1dinsxy + dinsxy = 0

Combine like terms: -1dinsxy + dinsxy = 0
-1cdosxy2 + cdosx2y + 0 = 0
-1cdosxy2 + cdosx2y = 0

Solving
-1cdosxy2 + cdosx2y = 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), 'cdosxy'.
cdosxy(-1y + x) = 0

Subproblem 1

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