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Simplifying (siny + -1ysinx) * dx + (cosx + xcosy + -1y) * dy = 0 Reorder the terms: (-1insxy + insy) * dx + (cosx + xcosy + -1y) * dy = 0 Reorder the terms for easier multiplication: dx(-1insxy + insy) + (cosx + xcosy + -1y) * dy = 0 (-1insxy * dx + insy * dx) + (cosx + xcosy + -1y) * dy = 0 Reorder the terms: (dinsxy + -1dinsx2y) + (cosx + xcosy + -1y) * dy = 0 (dinsxy + -1dinsx2y) + (cosx + xcosy + -1y) * dy = 0 Reorder the terms for easier multiplication: dinsxy + -1dinsx2y + dy(cosx + cosxy + -1y) = 0 dinsxy + -1dinsx2y + (cosx * dy + cosxy * dy + -1y * dy) = 0 dinsxy + -1dinsx2y + (cdosxy + cdosxy2 + -1dy2) = 0 Reorder the terms: cdosxy + cdosxy2 + dinsxy + -1dinsx2y + -1dy2 = 0 Solving cdosxy + cdosxy2 + dinsxy + -1dinsx2y + -1dy2 = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1dinsxy' to each side of the equation. cdosxy + cdosxy2 + dinsxy + -1dinsx2y + -1dinsxy + -1dy2 = 0 + -1dinsxy Reorder the terms: cdosxy + cdosxy2 + dinsxy + -1dinsxy + -1dinsx2y + -1dy2 = 0 + -1dinsxy Combine like terms: dinsxy + -1dinsxy = 0 cdosxy + cdosxy2 + 0 + -1dinsx2y + -1dy2 = 0 + -1dinsxy cdosxy + cdosxy2 + -1dinsx2y + -1dy2 = 0 + -1dinsxy Remove the zero: cdosxy + cdosxy2 + -1dinsx2y + -1dy2 = -1dinsxy Add 'dinsx2y' to each side of the equation. cdosxy + cdosxy2 + -1dinsx2y + dinsx2y + -1dy2 = -1dinsxy + dinsx2y Combine like terms: -1dinsx2y + dinsx2y = 0 cdosxy + cdosxy2 + 0 + -1dy2 = -1dinsxy + dinsx2y cdosxy + cdosxy2 + -1dy2 = -1dinsxy + dinsx2y Add 'dy2' to each side of the equation. cdosxy + cdosxy2 + -1dy2 + dy2 = -1dinsxy + dinsx2y + dy2 Combine like terms: -1dy2 + dy2 = 0 cdosxy + cdosxy2 + 0 = -1dinsxy + dinsx2y + dy2 cdosxy + cdosxy2 = -1dinsxy + dinsx2y + dy2 Reorder the terms: cdosxy + cdosxy2 + dinsxy + -1dinsx2y + -1dy2 = -1dinsxy + dinsxy + dinsx2y + -1dinsx2y + dy2 + -1dy2 Combine like terms: -1dinsxy + dinsxy = 0 cdosxy + cdosxy2 + dinsxy + -1dinsx2y + -1dy2 = 0 + dinsx2y + -1dinsx2y + dy2 + -1dy2 cdosxy + cdosxy2 + dinsxy + -1dinsx2y + -1dy2 = dinsx2y + -1dinsx2y + dy2 + -1dy2 Combine like terms: dinsx2y + -1dinsx2y = 0 cdosxy + cdosxy2 + dinsxy + -1dinsx2y + -1dy2 = 0 + dy2 + -1dy2 cdosxy + cdosxy2 + dinsxy + -1dinsx2y + -1dy2 = dy2 + -1dy2 Combine like terms: dy2 + -1dy2 = 0 cdosxy + cdosxy2 + dinsxy + -1dinsx2y + -1dy2 = 0 Factor out the Greatest Common Factor (GCF), 'dy'. dy(cosx + cosxy + insx + -1insx2 + -1y) = 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 '(cosx + cosxy + insx + -1insx2 + -1y)' equal to zero and attempt to solve: Simplifying cosx + cosxy + insx + -1insx2 + -1y = 0 Solving cosx + cosxy + insx + -1insx2 + -1y = 0 Move all terms containing c to the left, all other terms to the right. Add '-1insx' to each side of the equation. cosx + cosxy + insx + -1insx2 + -1insx + -1y = 0 + -1insx Reorder the terms: cosx + cosxy + insx + -1insx + -1insx2 + -1y = 0 + -1insx Combine like terms: insx + -1insx = 0 cosx + cosxy + 0 + -1insx2 + -1y = 0 + -1insx cosx + cosxy + -1insx2 + -1y = 0 + -1insx Remove the zero: cosx + cosxy + -1insx2 + -1y = -1insx Add 'insx2' to each side of the equation. cosx + cosxy + -1insx2 + insx2 + -1y = -1insx + insx2 Combine like terms: -1insx2 + insx2 = 0 cosx + cosxy + 0 + -1y = -1insx + insx2 cosx + cosxy + -1y = -1insx + insx2 Add 'y' to each side of the equation. cosx + cosxy + -1y + y = -1insx + insx2 + y Combine like terms: -1y + y = 0 cosx + cosxy + 0 = -1insx + insx2 + y cosx + cosxy = -1insx + insx2 + 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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