solve(3y^2-x)dx+(2y^3-6xy)dy=0

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


Simplifying
solve(3y2 + -1x) * dx + (2y3 + -6xy) * dy = 0

Reorder the terms:
elosv(-1x + 3y2) * dx + (2y3 + -6xy) * dy = 0

Reorder the terms for easier multiplication:
elosv * dx(-1x + 3y2) + (2y3 + -6xy) * dy = 0

Multiply elosv * dx
delosvx(-1x + 3y2) + (2y3 + -6xy) * dy = 0
(-1x * delosvx + 3y2 * delosvx) + (2y3 + -6xy) * dy = 0

Reorder the terms:
(3delosvxy2 + -1delosvx2) + (2y3 + -6xy) * dy = 0
(3delosvxy2 + -1delosvx2) + (2y3 + -6xy) * dy = 0

Reorder the terms:
3delosvxy2 + -1delosvx2 + (-6xy + 2y3) * dy = 0

Reorder the terms for easier multiplication:
3delosvxy2 + -1delosvx2 + dy(-6xy + 2y3) = 0
3delosvxy2 + -1delosvx2 + (-6xy * dy + 2y3 * dy) = 0
3delosvxy2 + -1delosvx2 + (-6dxy2 + 2dy4) = 0

Solving
3delosvxy2 + -1delosvx2 + -6dxy2 + 2dy4 = 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), 'd'.
d(3elosvxy2 + -1elosvx2 + -6xy2 + 2y4) = 0

Subproblem 1

Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0

Subproblem 2

Set the factor '(3elosvxy2 + -1elosvx2 + -6xy2 + 2y4)' equal to zero and attempt to solve: Simplifying 3elosvxy2 + -1elosvx2 + -6xy2 + 2y4 = 0 Solving 3elosvxy2 + -1elosvx2 + -6xy2 + 2y4 = 0 Move all terms containing d to the left, all other terms to the right. Add '-3elosvxy2' to each side of the equation. 3elosvxy2 + -1elosvx2 + -6xy2 + -3elosvxy2 + 2y4 = 0 + -3elosvxy2 Reorder the terms: 3elosvxy2 + -3elosvxy2 + -1elosvx2 + -6xy2 + 2y4 = 0 + -3elosvxy2 Combine like terms: 3elosvxy2 + -3elosvxy2 = 0 0 + -1elosvx2 + -6xy2 + 2y4 = 0 + -3elosvxy2 -1elosvx2 + -6xy2 + 2y4 = 0 + -3elosvxy2 Remove the zero: -1elosvx2 + -6xy2 + 2y4 = -3elosvxy2 Add 'elosvx2' to each side of the equation. -1elosvx2 + -6xy2 + elosvx2 + 2y4 = -3elosvxy2 + elosvx2 Reorder the terms: -1elosvx2 + elosvx2 + -6xy2 + 2y4 = -3elosvxy2 + elosvx2 Combine like terms: -1elosvx2 + elosvx2 = 0 0 + -6xy2 + 2y4 = -3elosvxy2 + elosvx2 -6xy2 + 2y4 = -3elosvxy2 + elosvx2 Add '6xy2' to each side of the equation. -6xy2 + 6xy2 + 2y4 = -3elosvxy2 + elosvx2 + 6xy2 Combine like terms: -6xy2 + 6xy2 = 0 0 + 2y4 = -3elosvxy2 + elosvx2 + 6xy2 2y4 = -3elosvxy2 + elosvx2 + 6xy2 Add '-2y4' to each side of the equation. 2y4 + -2y4 = -3elosvxy2 + elosvx2 + 6xy2 + -2y4 Combine like terms: 2y4 + -2y4 = 0 0 = -3elosvxy2 + elosvx2 + 6xy2 + -2y4 Simplifying 0 = -3elosvxy2 + elosvx2 + 6xy2 + -2y4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

d = {0}

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