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Simplifying x(1 + -1x2) * dy + (2x2y + -1y + -1ax3) * dx = 0 Reorder the terms for easier multiplication: x * dy(1 + -1x2) + (2x2y + -1y + -1ax3) * dx = 0 Multiply x * dy dxy(1 + -1x2) + (2x2y + -1y + -1ax3) * dx = 0 (1 * dxy + -1x2 * dxy) + (2x2y + -1y + -1ax3) * dx = 0 (1dxy + -1dx3y) + (2x2y + -1y + -1ax3) * dx = 0 Reorder the terms: 1dxy + -1dx3y + (-1ax3 + 2x2y + -1y) * dx = 0 Reorder the terms for easier multiplication: 1dxy + -1dx3y + dx(-1ax3 + 2x2y + -1y) = 0 1dxy + -1dx3y + (-1ax3 * dx + 2x2y * dx + -1y * dx) = 0 Reorder the terms: 1dxy + -1dx3y + (-1adx4 + -1dxy + 2dx3y) = 0 1dxy + -1dx3y + (-1adx4 + -1dxy + 2dx3y) = 0 Reorder the terms: -1adx4 + 1dxy + -1dxy + -1dx3y + 2dx3y = 0 Combine like terms: 1dxy + -1dxy = 0 -1adx4 + 0 + -1dx3y + 2dx3y = 0 -1adx4 + -1dx3y + 2dx3y = 0 Combine like terms: -1dx3y + 2dx3y = 1dx3y -1adx4 + 1dx3y = 0 Solving -1adx4 + 1dx3y = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1dx3y' to each side of the equation. -1adx4 + 1dx3y + -1dx3y = 0 + -1dx3y Combine like terms: 1dx3y + -1dx3y = 0 -1adx4 + 0 = 0 + -1dx3y -1adx4 = 0 + -1dx3y Remove the zero: -1adx4 = -1dx3y Divide each side by '-1dx4'. a = x-1y Simplifying a = x-1y
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