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Simplifying [-1(8sin(y) + 8ysin(x))] * dx + (8cos(x) + -8xcos(y) + 8y) * dy = 0 Multiply ins * y [-1(8insy + 8ysin(x))] * dx + (8cos(x) + -8xcos(y) + 8y) * dy = 0 Multiply insy * x [-1(8insy + 8insxy)] * dx + (8cos(x) + -8xcos(y) + 8y) * dy = 0 Reorder the terms: [-1(8insxy + 8insy)] * dx + (8cos(x) + -8xcos(y) + 8y) * dy = 0 [(8insxy * -1 + 8insy * -1)] * dx + (8cos(x) + -8xcos(y) + 8y) * dy = 0 [(-8insxy + -8insy)] * dx + (8cos(x) + -8xcos(y) + 8y) * dy = 0 Reorder the terms for easier multiplication: dx[-8insxy + -8insy] + (8cos(x) + -8xcos(y) + 8y) * dy = 0 [-8insxy * dx + -8insy * dx] + (8cos(x) + -8xcos(y) + 8y) * dy = 0 Reorder the terms: [-8dinsxy + -8dinsx2y] + (8cos(x) + -8xcos(y) + 8y) * dy = 0 [-8dinsxy + -8dinsx2y] + (8cos(x) + -8xcos(y) + 8y) * dy = 0 Multiply cos * x -8dinsxy + -8dinsx2y + (8cosx + -8xcos(y) + 8y) * dy = 0 Multiply cosx * y -8dinsxy + -8dinsx2y + (8cosx + -8cosxy + 8y) * dy = 0 Reorder the terms for easier multiplication: -8dinsxy + -8dinsx2y + dy(8cosx + -8cosxy + 8y) = 0 -8dinsxy + -8dinsx2y + (8cosx * dy + -8cosxy * dy + 8y * dy) = 0 -8dinsxy + -8dinsx2y + (8cdosxy + -8cdosxy2 + 8dy2) = 0 Reorder the terms: 8cdosxy + -8cdosxy2 + -8dinsxy + -8dinsx2y + 8dy2 = 0 Solving 8cdosxy + -8cdosxy2 + -8dinsxy + -8dinsx2y + 8dy2 = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '8dinsxy' to each side of the equation. 8cdosxy + -8cdosxy2 + -8dinsxy + -8dinsx2y + 8dinsxy + 8dy2 = 0 + 8dinsxy Reorder the terms: 8cdosxy + -8cdosxy2 + -8dinsxy + 8dinsxy + -8dinsx2y + 8dy2 = 0 + 8dinsxy Combine like terms: -8dinsxy + 8dinsxy = 0 8cdosxy + -8cdosxy2 + 0 + -8dinsx2y + 8dy2 = 0 + 8dinsxy 8cdosxy + -8cdosxy2 + -8dinsx2y + 8dy2 = 0 + 8dinsxy Remove the zero: 8cdosxy + -8cdosxy2 + -8dinsx2y + 8dy2 = 8dinsxy Add '8dinsx2y' to each side of the equation. 8cdosxy + -8cdosxy2 + -8dinsx2y + 8dinsx2y + 8dy2 = 8dinsxy + 8dinsx2y Combine like terms: -8dinsx2y + 8dinsx2y = 0 8cdosxy + -8cdosxy2 + 0 + 8dy2 = 8dinsxy + 8dinsx2y 8cdosxy + -8cdosxy2 + 8dy2 = 8dinsxy + 8dinsx2y Add '-8dy2' to each side of the equation. 8cdosxy + -8cdosxy2 + 8dy2 + -8dy2 = 8dinsxy + 8dinsx2y + -8dy2 Combine like terms: 8dy2 + -8dy2 = 0 8cdosxy + -8cdosxy2 + 0 = 8dinsxy + 8dinsx2y + -8dy2 8cdosxy + -8cdosxy2 = 8dinsxy + 8dinsx2y + -8dy2 Reorder the terms: 8cdosxy + -8cdosxy2 + -8dinsxy + -8dinsx2y + 8dy2 = 8dinsxy + -8dinsxy + 8dinsx2y + -8dinsx2y + -8dy2 + 8dy2 Combine like terms: 8dinsxy + -8dinsxy = 0 8cdosxy + -8cdosxy2 + -8dinsxy + -8dinsx2y + 8dy2 = 0 + 8dinsx2y + -8dinsx2y + -8dy2 + 8dy2 8cdosxy + -8cdosxy2 + -8dinsxy + -8dinsx2y + 8dy2 = 8dinsx2y + -8dinsx2y + -8dy2 + 8dy2 Combine like terms: 8dinsx2y + -8dinsx2y = 0 8cdosxy + -8cdosxy2 + -8dinsxy + -8dinsx2y + 8dy2 = 0 + -8dy2 + 8dy2 8cdosxy + -8cdosxy2 + -8dinsxy + -8dinsx2y + 8dy2 = -8dy2 + 8dy2 Combine like terms: -8dy2 + 8dy2 = 0 8cdosxy + -8cdosxy2 + -8dinsxy + -8dinsx2y + 8dy2 = 0 Factor out the Greatest Common Factor (GCF), '8dy'. 8dy(cosx + -1cosxy + -1insx + -1insx2 + y) = 0 Ignore the factor 8.Subproblem 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 + -1cosxy + -1insx + -1insx2 + y)' equal to zero and attempt to solve: Simplifying cosx + -1cosxy + -1insx + -1insx2 + y = 0 Solving cosx + -1cosxy + -1insx + -1insx2 + y = 0 Move all terms containing c to the left, all other terms to the right. Add 'insx' to each side of the equation. cosx + -1cosxy + -1insx + -1insx2 + insx + y = 0 + insx Reorder the terms: cosx + -1cosxy + -1insx + insx + -1insx2 + y = 0 + insx Combine like terms: -1insx + insx = 0 cosx + -1cosxy + 0 + -1insx2 + y = 0 + insx cosx + -1cosxy + -1insx2 + y = 0 + insx Remove the zero: cosx + -1cosxy + -1insx2 + y = insx Add 'insx2' to each side of the equation. cosx + -1cosxy + -1insx2 + insx2 + y = insx + insx2 Combine like terms: -1insx2 + insx2 = 0 cosx + -1cosxy + 0 + y = insx + insx2 cosx + -1cosxy + y = insx + insx2 Add '-1y' to each side of the equation. cosx + -1cosxy + y + -1y = insx + insx2 + -1y Combine like terms: y + -1y = 0 cosx + -1cosxy + 0 = insx + insx2 + -1y cosx + -1cosxy = insx + insx2 + -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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