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Simplifying (xy2 + -1tany) * dx + (x2y + -1xsec2y) * dy = 0 Reorder the terms: (-1anty + xy2) * dx + (x2y + -1xsec2y) * dy = 0 Reorder the terms for easier multiplication: dx(-1anty + xy2) + (x2y + -1xsec2y) * dy = 0 (-1anty * dx + xy2 * dx) + (x2y + -1xsec2y) * dy = 0 (-1adntxy + dx2y2) + (x2y + -1xsec2y) * dy = 0 Reorder the terms: -1adntxy + dx2y2 + (-1c2esxy + x2y) * dy = 0 Reorder the terms for easier multiplication: -1adntxy + dx2y2 + dy(-1c2esxy + x2y) = 0 -1adntxy + dx2y2 + (-1c2esxy * dy + x2y * dy) = 0 -1adntxy + dx2y2 + (-1c2desxy2 + dx2y2) = 0 Reorder the terms: -1adntxy + -1c2desxy2 + dx2y2 + dx2y2 = 0 Combine like terms: dx2y2 + dx2y2 = 2dx2y2 -1adntxy + -1c2desxy2 + 2dx2y2 = 0 Solving -1adntxy + -1c2desxy2 + 2dx2y2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add 'c2desxy2' to each side of the equation. -1adntxy + -1c2desxy2 + c2desxy2 + 2dx2y2 = 0 + c2desxy2 Combine like terms: -1c2desxy2 + c2desxy2 = 0 -1adntxy + 0 + 2dx2y2 = 0 + c2desxy2 -1adntxy + 2dx2y2 = 0 + c2desxy2 Remove the zero: -1adntxy + 2dx2y2 = c2desxy2 Add '-2dx2y2' to each side of the equation. -1adntxy + 2dx2y2 + -2dx2y2 = c2desxy2 + -2dx2y2 Combine like terms: 2dx2y2 + -2dx2y2 = 0 -1adntxy + 0 = c2desxy2 + -2dx2y2 -1adntxy = c2desxy2 + -2dx2y2 Divide each side by '-1dntxy'. a = -1c2en-1st-1y + 2n-1t-1xy Simplifying a = -1c2en-1st-1y + 2n-1t-1xy
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