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Simplifying [1 + ytan(xy)] * dx + xtan(xy) * dy = 0 Multiply anty * xy [1 + antxy2] * dx + xtan(xy) * dy = 0 Reorder the terms for easier multiplication: dx[1 + antxy2] + xtan(xy) * dy = 0 [1 * dx + antxy2 * dx] + xtan(xy) * dy = 0 Reorder the terms: [adntx2y2 + 1dx] + xtan(xy) * dy = 0 [adntx2y2 + 1dx] + xtan(xy) * dy = 0 Multiply antx * xy adntx2y2 + 1dx + antx2y * dy = 0 Multiply antx2y * dy adntx2y2 + 1dx + adntx2y2 = 0 Reorder the terms: adntx2y2 + adntx2y2 + 1dx = 0 Combine like terms: adntx2y2 + adntx2y2 = 2adntx2y2 2adntx2y2 + 1dx = 0 Solving 2adntx2y2 + 1dx = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1dx' to each side of the equation. 2adntx2y2 + 1dx + -1dx = 0 + -1dx Combine like terms: 1dx + -1dx = 0 2adntx2y2 + 0 = 0 + -1dx 2adntx2y2 = 0 + -1dx Remove the zero: 2adntx2y2 = -1dx Divide each side by '2dntx2y2'. a = -0.5n-1t-1x-1y-2 Simplifying a = -0.5n-1t-1x-1y-2
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