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Simplifying (1 + 3xsiny) * dx + -1(x2cosy) * dy = 0 Reorder the terms for easier multiplication: dx(1 + 3insxy) + -1(x2cosy) * dy = 0 (1 * dx + 3insxy * dx) + -1(x2cosy) * dy = 0 Reorder the terms: (3dinsx2y + 1dx) + -1(x2cosy) * dy = 0 (3dinsx2y + 1dx) + -1(x2cosy) * dy = 0 Multiply cosx2y * dy 3dinsx2y + 1dx + -1cdosx2y2 = 0 Reorder the terms: -1cdosx2y2 + 3dinsx2y + 1dx = 0 Solving -1cdosx2y2 + 3dinsx2y + 1dx = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3dinsx2y' to each side of the equation. -1cdosx2y2 + 3dinsx2y + -3dinsx2y + 1dx = 0 + -3dinsx2y Combine like terms: 3dinsx2y + -3dinsx2y = 0 -1cdosx2y2 + 0 + 1dx = 0 + -3dinsx2y -1cdosx2y2 + 1dx = 0 + -3dinsx2y Remove the zero: -1cdosx2y2 + 1dx = -3dinsx2y Add '-1dx' to each side of the equation. -1cdosx2y2 + 1dx + -1dx = -3dinsx2y + -1dx Combine like terms: 1dx + -1dx = 0 -1cdosx2y2 + 0 = -3dinsx2y + -1dx -1cdosx2y2 = -3dinsx2y + -1dx Divide each side by '-1dosx2y2'. c = 3ino-1y-1 + o-1s-1x-1y-2 Simplifying c = 3ino-1y-1 + o-1s-1x-1y-2
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