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

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


Simplifying
solve(3xy + y2) * dx + (x2 + xy) * dy = 0

Reorder the terms for easier multiplication:
elosv * dx(3xy + y2) + (x2 + xy) * dy = 0

Multiply elosv * dx
delosvx(3xy + y2) + (x2 + xy) * dy = 0
(3xy * delosvx + y2 * delosvx) + (x2 + xy) * dy = 0

Reorder the terms:
(delosvxy2 + 3delosvx2y) + (x2 + xy) * dy = 0
(delosvxy2 + 3delosvx2y) + (x2 + xy) * dy = 0

Reorder the terms:
delosvxy2 + 3delosvx2y + (xy + x2) * dy = 0

Reorder the terms for easier multiplication:
delosvxy2 + 3delosvx2y + dy(xy + x2) = 0
delosvxy2 + 3delosvx2y + (xy * dy + x2 * dy) = 0
delosvxy2 + 3delosvx2y + (dxy2 + dx2y) = 0

Solving
delosvxy2 + 3delosvx2y + dxy2 + dx2y = 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), 'dxy'.
dxy(elosvy + 3elosvx + y + x) = 0

Subproblem 1

Set the factor 'dxy' equal to zero and attempt to solve: Simplifying dxy = 0 Solving dxy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dxy = 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 '(elosvy + 3elosvx + y + x)' equal to zero and attempt to solve: Simplifying elosvy + 3elosvx + y + x = 0 Reorder the terms: 3elosvx + elosvy + x + y = 0 Solving 3elosvx + elosvy + x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-3elosvx' to each side of the equation. 3elosvx + elosvy + x + -3elosvx + y = 0 + -3elosvx Reorder the terms: 3elosvx + -3elosvx + elosvy + x + y = 0 + -3elosvx Combine like terms: 3elosvx + -3elosvx = 0 0 + elosvy + x + y = 0 + -3elosvx elosvy + x + y = 0 + -3elosvx Remove the zero: elosvy + x + y = -3elosvx Add '-1elosvy' to each side of the equation. elosvy + x + -1elosvy + y = -3elosvx + -1elosvy Reorder the terms: elosvy + -1elosvy + x + y = -3elosvx + -1elosvy Combine like terms: elosvy + -1elosvy = 0 0 + x + y = -3elosvx + -1elosvy x + y = -3elosvx + -1elosvy Add '-1x' to each side of the equation. x + -1x + y = -3elosvx + -1elosvy + -1x Combine like terms: x + -1x = 0 0 + y = -3elosvx + -1elosvy + -1x y = -3elosvx + -1elosvy + -1x Add '-1y' to each side of the equation. y + -1y = -3elosvx + -1elosvy + -1x + -1y Combine like terms: y + -1y = 0 0 = -3elosvx + -1elosvy + -1x + -1y Simplifying 0 = -3elosvx + -1elosvy + -1x + -1y 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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