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

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


Simplifying
(x2 + xy + 3y2) * dx + -1(x2 + 2xy) * dy = 0

Reorder the terms:
(xy + x2 + 3y2) * dx + -1(x2 + 2xy) * dy = 0

Reorder the terms for easier multiplication:
dx(xy + x2 + 3y2) + -1(x2 + 2xy) * dy = 0
(xy * dx + x2 * dx + 3y2 * dx) + -1(x2 + 2xy) * dy = 0

Reorder the terms:
(3dxy2 + dx2y + dx3) + -1(x2 + 2xy) * dy = 0
(3dxy2 + dx2y + dx3) + -1(x2 + 2xy) * dy = 0

Reorder the terms:
3dxy2 + dx2y + dx3 + -1(2xy + x2) * dy = 0

Reorder the terms for easier multiplication:
3dxy2 + dx2y + dx3 + -1dy(2xy + x2) = 0
3dxy2 + dx2y + dx3 + (2xy * -1dy + x2 * -1dy) = 0
3dxy2 + dx2y + dx3 + (-2dxy2 + -1dx2y) = 0

Reorder the terms:
3dxy2 + -2dxy2 + dx2y + -1dx2y + dx3 = 0

Combine like terms: 3dxy2 + -2dxy2 = 1dxy2
1dxy2 + dx2y + -1dx2y + dx3 = 0

Combine like terms: dx2y + -1dx2y = 0
1dxy2 + 0 + dx3 = 0
1dxy2 + dx3 = 0

Solving
1dxy2 + dx3 = 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), 'dx'.
dx(y2 + x2) = 0

Subproblem 1

Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 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 '(y2 + x2)' equal to zero and attempt to solve: Simplifying y2 + x2 = 0 Reorder the terms: x2 + y2 = 0 Solving x2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + -1x2 + y2 = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + y2 = 0 + -1x2 y2 = 0 + -1x2 Remove the zero: y2 = -1x2 Add '-1y2' to each side of the equation. y2 + -1y2 = -1x2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1x2 + -1y2 Simplifying 0 = -1x2 + -1y2 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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