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Simplifying 6y2dx + -1x(ax3 + y) * dy = 0 Reorder the terms for easier multiplication: 6dxy2 + -1x * dy(ax3 + y) = 0 Multiply x * dy 6dxy2 + -1dxy(ax3 + y) = 0 6dxy2 + (ax3 * -1dxy + y * -1dxy) = 0 6dxy2 + (-1adx4y + -1dxy2) = 0 Reorder the terms: -1adx4y + 6dxy2 + -1dxy2 = 0 Combine like terms: 6dxy2 + -1dxy2 = 5dxy2 -1adx4y + 5dxy2 = 0 Solving -1adx4y + 5dxy2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5dxy2' to each side of the equation. -1adx4y + 5dxy2 + -5dxy2 = 0 + -5dxy2 Combine like terms: 5dxy2 + -5dxy2 = 0 -1adx4y + 0 = 0 + -5dxy2 -1adx4y = 0 + -5dxy2 Remove the zero: -1adx4y = -5dxy2 Divide each side by '-1dx4y'. a = 5x-3y Simplifying a = 5x-3y
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