solve(2y^2-2y^3)dx+(4y^3-6y^2*x+2yx^2)dy=0

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Solution for solve(2y^2-2y^3)dx+(4y^3-6y^2*x+2yx^2)dy=0 equation:


Simplifying
solve(2y2 + -2y3) * dx + (4y3 + -6y2 * x + 2yx2) * dy = 0

Reorder the terms for easier multiplication:
elosv * dx(2y2 + -2y3) + (4y3 + -6y2 * x + 2yx2) * dy = 0

Multiply elosv * dx
delosvx(2y2 + -2y3) + (4y3 + -6y2 * x + 2yx2) * dy = 0
(2y2 * delosvx + -2y3 * delosvx) + (4y3 + -6y2 * x + 2yx2) * dy = 0
(2delosvxy2 + -2delosvxy3) + (4y3 + -6y2 * x + 2yx2) * dy = 0

Multiply y2 * x
2delosvxy2 + -2delosvxy3 + (4y3 + -6xy2 + 2yx2) * dy = 0

Reorder the terms:
2delosvxy2 + -2delosvxy3 + (-6xy2 + 2x2y + 4y3) * dy = 0

Reorder the terms for easier multiplication:
2delosvxy2 + -2delosvxy3 + dy(-6xy2 + 2x2y + 4y3) = 0
2delosvxy2 + -2delosvxy3 + (-6xy2 * dy + 2x2y * dy + 4y3 * dy) = 0
2delosvxy2 + -2delosvxy3 + (-6dxy3 + 2dx2y2 + 4dy4) = 0

Solving
2delosvxy2 + -2delosvxy3 + -6dxy3 + 2dx2y2 + 4dy4 = 0

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Factor out the Greatest Common Factor (GCF), '2dy2'.
2dy2(elosvx + -1elosvxy + -3xy + x2 + 2y2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'dy2' equal to zero and attempt to solve: Simplifying dy2 = 0 Solving dy2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy2 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(elosvx + -1elosvxy + -3xy + x2 + 2y2)' equal to zero and attempt to solve: Simplifying elosvx + -1elosvxy + -3xy + x2 + 2y2 = 0 Solving elosvx + -1elosvxy + -3xy + x2 + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1elosvx' to each side of the equation. elosvx + -1elosvxy + -3xy + x2 + -1elosvx + 2y2 = 0 + -1elosvx Reorder the terms: elosvx + -1elosvx + -1elosvxy + -3xy + x2 + 2y2 = 0 + -1elosvx Combine like terms: elosvx + -1elosvx = 0 0 + -1elosvxy + -3xy + x2 + 2y2 = 0 + -1elosvx -1elosvxy + -3xy + x2 + 2y2 = 0 + -1elosvx Remove the zero: -1elosvxy + -3xy + x2 + 2y2 = -1elosvx Add 'elosvxy' to each side of the equation. -1elosvxy + -3xy + x2 + elosvxy + 2y2 = -1elosvx + elosvxy Reorder the terms: -1elosvxy + elosvxy + -3xy + x2 + 2y2 = -1elosvx + elosvxy Combine like terms: -1elosvxy + elosvxy = 0 0 + -3xy + x2 + 2y2 = -1elosvx + elosvxy -3xy + x2 + 2y2 = -1elosvx + elosvxy Add '3xy' to each side of the equation. -3xy + x2 + 3xy + 2y2 = -1elosvx + elosvxy + 3xy Reorder the terms: -3xy + 3xy + x2 + 2y2 = -1elosvx + elosvxy + 3xy Combine like terms: -3xy + 3xy = 0 0 + x2 + 2y2 = -1elosvx + elosvxy + 3xy x2 + 2y2 = -1elosvx + elosvxy + 3xy Add '-1x2' to each side of the equation. x2 + -1x2 + 2y2 = -1elosvx + elosvxy + 3xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 2y2 = -1elosvx + elosvxy + 3xy + -1x2 2y2 = -1elosvx + elosvxy + 3xy + -1x2 Add '-2y2' to each side of the equation. 2y2 + -2y2 = -1elosvx + elosvxy + 3xy + -1x2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = -1elosvx + elosvxy + 3xy + -1x2 + -2y2 Simplifying 0 = -1elosvx + elosvxy + 3xy + -1x2 + -2y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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