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Simplifying y(1 + x) * dx = x(1 + x) * dy Reorder the terms for easier multiplication: y * dx(1 + x) = x(1 + x) * dy Multiply y * dx dxy(1 + x) = x(1 + x) * dy (1 * dxy + x * dxy) = x(1 + x) * dy (1dxy + dx2y) = x(1 + x) * dy Reorder the terms for easier multiplication: 1dxy + dx2y = x * dy(1 + x) Multiply x * dy 1dxy + dx2y = dxy(1 + x) 1dxy + dx2y = (1 * dxy + x * dxy) 1dxy + dx2y = (1dxy + dx2y) Add '-1dxy' to each side of the equation. 1dxy + -1dxy + dx2y = 1dxy + -1dxy + dx2y Combine like terms: 1dxy + -1dxy = 0 0 + dx2y = 1dxy + -1dxy + dx2y dx2y = 1dxy + -1dxy + dx2y Combine like terms: 1dxy + -1dxy = 0 dx2y = 0 + dx2y dx2y = dx2y Add '-1dx2y' to each side of the equation. dx2y + -1dx2y = dx2y + -1dx2y Combine like terms: dx2y + -1dx2y = 0 0 = dx2y + -1dx2y Combine like terms: dx2y + -1dx2y = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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