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Simplifying (2xy + -1tany) * dx + (x2 + -1xsec2y) * dy = 0 Reorder the terms: (-1anty + 2xy) * dx + (x2 + -1xsec2y) * dy = 0 Reorder the terms for easier multiplication: dx(-1anty + 2xy) + (x2 + -1xsec2y) * dy = 0 (-1anty * dx + 2xy * dx) + (x2 + -1xsec2y) * dy = 0 (-1adntxy + 2dx2y) + (x2 + -1xsec2y) * dy = 0 Reorder the terms: -1adntxy + 2dx2y + (-1c2esxy + x2) * dy = 0 Reorder the terms for easier multiplication: -1adntxy + 2dx2y + dy(-1c2esxy + x2) = 0 -1adntxy + 2dx2y + (-1c2esxy * dy + x2 * dy) = 0 -1adntxy + 2dx2y + (-1c2desxy2 + dx2y) = 0 Reorder the terms: -1adntxy + -1c2desxy2 + 2dx2y + dx2y = 0 Combine like terms: 2dx2y + dx2y = 3dx2y -1adntxy + -1c2desxy2 + 3dx2y = 0 Solving -1adntxy + -1c2desxy2 + 3dx2y = 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 + 3dx2y = 0 + c2desxy2 Combine like terms: -1c2desxy2 + c2desxy2 = 0 -1adntxy + 0 + 3dx2y = 0 + c2desxy2 -1adntxy + 3dx2y = 0 + c2desxy2 Remove the zero: -1adntxy + 3dx2y = c2desxy2 Add '-3dx2y' to each side of the equation. -1adntxy + 3dx2y + -3dx2y = c2desxy2 + -3dx2y Combine like terms: 3dx2y + -3dx2y = 0 -1adntxy + 0 = c2desxy2 + -3dx2y -1adntxy = c2desxy2 + -3dx2y Divide each side by '-1dntxy'. a = -1c2en-1st-1y + 3n-1t-1x Simplifying a = -1c2en-1st-1y + 3n-1t-1x
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