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Simplifying (2sin(y) + -3ysin(x)) * dx + (3cos(x) + 2xcos(y) + -4y) * dy = 0 Multiply ins * y (2insy + -3ysin(x)) * dx + (3cos(x) + 2xcos(y) + -4y) * dy = 0 Multiply insy * x (2insy + -3insxy) * dx + (3cos(x) + 2xcos(y) + -4y) * dy = 0 Reorder the terms: (-3insxy + 2insy) * dx + (3cos(x) + 2xcos(y) + -4y) * dy = 0 Reorder the terms for easier multiplication: dx(-3insxy + 2insy) + (3cos(x) + 2xcos(y) + -4y) * dy = 0 (-3insxy * dx + 2insy * dx) + (3cos(x) + 2xcos(y) + -4y) * dy = 0 Reorder the terms: (2dinsxy + -3dinsx2y) + (3cos(x) + 2xcos(y) + -4y) * dy = 0 (2dinsxy + -3dinsx2y) + (3cos(x) + 2xcos(y) + -4y) * dy = 0 Multiply cos * x 2dinsxy + -3dinsx2y + (3cosx + 2xcos(y) + -4y) * dy = 0 Multiply cosx * y 2dinsxy + -3dinsx2y + (3cosx + 2cosxy + -4y) * dy = 0 Reorder the terms for easier multiplication: 2dinsxy + -3dinsx2y + dy(3cosx + 2cosxy + -4y) = 0 2dinsxy + -3dinsx2y + (3cosx * dy + 2cosxy * dy + -4y * dy) = 0 2dinsxy + -3dinsx2y + (3cdosxy + 2cdosxy2 + -4dy2) = 0 Reorder the terms: 3cdosxy + 2cdosxy2 + 2dinsxy + -3dinsx2y + -4dy2 = 0 Solving 3cdosxy + 2cdosxy2 + 2dinsxy + -3dinsx2y + -4dy2 = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2dinsxy' to each side of the equation. 3cdosxy + 2cdosxy2 + 2dinsxy + -3dinsx2y + -2dinsxy + -4dy2 = 0 + -2dinsxy Reorder the terms: 3cdosxy + 2cdosxy2 + 2dinsxy + -2dinsxy + -3dinsx2y + -4dy2 = 0 + -2dinsxy Combine like terms: 2dinsxy + -2dinsxy = 0 3cdosxy + 2cdosxy2 + 0 + -3dinsx2y + -4dy2 = 0 + -2dinsxy 3cdosxy + 2cdosxy2 + -3dinsx2y + -4dy2 = 0 + -2dinsxy Remove the zero: 3cdosxy + 2cdosxy2 + -3dinsx2y + -4dy2 = -2dinsxy Add '3dinsx2y' to each side of the equation. 3cdosxy + 2cdosxy2 + -3dinsx2y + 3dinsx2y + -4dy2 = -2dinsxy + 3dinsx2y Combine like terms: -3dinsx2y + 3dinsx2y = 0 3cdosxy + 2cdosxy2 + 0 + -4dy2 = -2dinsxy + 3dinsx2y 3cdosxy + 2cdosxy2 + -4dy2 = -2dinsxy + 3dinsx2y Add '4dy2' to each side of the equation. 3cdosxy + 2cdosxy2 + -4dy2 + 4dy2 = -2dinsxy + 3dinsx2y + 4dy2 Combine like terms: -4dy2 + 4dy2 = 0 3cdosxy + 2cdosxy2 + 0 = -2dinsxy + 3dinsx2y + 4dy2 3cdosxy + 2cdosxy2 = -2dinsxy + 3dinsx2y + 4dy2 Reorder the terms: 3cdosxy + 2cdosxy2 + 2dinsxy + -3dinsx2y + -4dy2 = -2dinsxy + 2dinsxy + 3dinsx2y + -3dinsx2y + 4dy2 + -4dy2 Combine like terms: -2dinsxy + 2dinsxy = 0 3cdosxy + 2cdosxy2 + 2dinsxy + -3dinsx2y + -4dy2 = 0 + 3dinsx2y + -3dinsx2y + 4dy2 + -4dy2 3cdosxy + 2cdosxy2 + 2dinsxy + -3dinsx2y + -4dy2 = 3dinsx2y + -3dinsx2y + 4dy2 + -4dy2 Combine like terms: 3dinsx2y + -3dinsx2y = 0 3cdosxy + 2cdosxy2 + 2dinsxy + -3dinsx2y + -4dy2 = 0 + 4dy2 + -4dy2 3cdosxy + 2cdosxy2 + 2dinsxy + -3dinsx2y + -4dy2 = 4dy2 + -4dy2 Combine like terms: 4dy2 + -4dy2 = 0 3cdosxy + 2cdosxy2 + 2dinsxy + -3dinsx2y + -4dy2 = 0 Factor out the Greatest Common Factor (GCF), 'dy'. dy(3cosx + 2cosxy + 2insx + -3insx2 + -4y) = 0Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing c to the left, all other terms to the right. Add '-1dy' to each side of the equation. dy + -1dy = 0 + -1dy Remove the zero: 0 = -1dy Simplifying 0 = -1dy 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 '(3cosx + 2cosxy + 2insx + -3insx2 + -4y)' equal to zero and attempt to solve: Simplifying 3cosx + 2cosxy + 2insx + -3insx2 + -4y = 0 Solving 3cosx + 2cosxy + 2insx + -3insx2 + -4y = 0 Move all terms containing c to the left, all other terms to the right. Add '-2insx' to each side of the equation. 3cosx + 2cosxy + 2insx + -3insx2 + -2insx + -4y = 0 + -2insx Reorder the terms: 3cosx + 2cosxy + 2insx + -2insx + -3insx2 + -4y = 0 + -2insx Combine like terms: 2insx + -2insx = 0 3cosx + 2cosxy + 0 + -3insx2 + -4y = 0 + -2insx 3cosx + 2cosxy + -3insx2 + -4y = 0 + -2insx Remove the zero: 3cosx + 2cosxy + -3insx2 + -4y = -2insx Add '3insx2' to each side of the equation. 3cosx + 2cosxy + -3insx2 + 3insx2 + -4y = -2insx + 3insx2 Combine like terms: -3insx2 + 3insx2 = 0 3cosx + 2cosxy + 0 + -4y = -2insx + 3insx2 3cosx + 2cosxy + -4y = -2insx + 3insx2 Add '4y' to each side of the equation. 3cosx + 2cosxy + -4y + 4y = -2insx + 3insx2 + 4y Combine like terms: -4y + 4y = 0 3cosx + 2cosxy + 0 = -2insx + 3insx2 + 4y 3cosx + 2cosxy = -2insx + 3insx2 + 4y 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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