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Simplifying [2x + ycos(xy)] * dx + xcos(xy) * dy = 0 Multiply cosy * xy [2x + cosxy2] * dx + xcos(xy) * dy = 0 Reorder the terms: [cosxy2 + 2x] * dx + xcos(xy) * dy = 0 Reorder the terms for easier multiplication: dx[cosxy2 + 2x] + xcos(xy) * dy = 0 [cosxy2 * dx + 2x * dx] + xcos(xy) * dy = 0 [cdosx2y2 + 2dx2] + xcos(xy) * dy = 0 Multiply cosx * xy cdosx2y2 + 2dx2 + cosx2y * dy = 0 Multiply cosx2y * dy cdosx2y2 + 2dx2 + cdosx2y2 = 0 Reorder the terms: cdosx2y2 + cdosx2y2 + 2dx2 = 0 Combine like terms: cdosx2y2 + cdosx2y2 = 2cdosx2y2 2cdosx2y2 + 2dx2 = 0 Solving 2cdosx2y2 + 2dx2 = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2dx2' to each side of the equation. 2cdosx2y2 + 2dx2 + -2dx2 = 0 + -2dx2 Combine like terms: 2dx2 + -2dx2 = 0 2cdosx2y2 + 0 = 0 + -2dx2 2cdosx2y2 = 0 + -2dx2 Remove the zero: 2cdosx2y2 = -2dx2 Divide each side by '2dosx2y2'. c = -1o-1s-1y-2 Simplifying c = -1o-1s-1y-2
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