(3x^2+2y+2)dx-(x^3+2xy+4y)dy=0

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Solution for (3x^2+2y+2)dx-(x^3+2xy+4y)dy=0 equation:


Simplifying
(3x2 + 2y + 2) * dx + -1(x3 + 2xy + 4y) * dy = 0

Reorder the terms:
(2 + 3x2 + 2y) * dx + -1(x3 + 2xy + 4y) * dy = 0

Reorder the terms for easier multiplication:
dx(2 + 3x2 + 2y) + -1(x3 + 2xy + 4y) * dy = 0
(2 * dx + 3x2 * dx + 2y * dx) + -1(x3 + 2xy + 4y) * dy = 0

Reorder the terms:
(2dx + 2dxy + 3dx3) + -1(x3 + 2xy + 4y) * dy = 0
(2dx + 2dxy + 3dx3) + -1(x3 + 2xy + 4y) * dy = 0

Reorder the terms:
2dx + 2dxy + 3dx3 + -1(2xy + x3 + 4y) * dy = 0

Reorder the terms for easier multiplication:
2dx + 2dxy + 3dx3 + -1dy(2xy + x3 + 4y) = 0
2dx + 2dxy + 3dx3 + (2xy * -1dy + x3 * -1dy + 4y * -1dy) = 0
2dx + 2dxy + 3dx3 + (-2dxy2 + -1dx3y + -4dy2) = 0

Reorder the terms:
2dx + 2dxy + -2dxy2 + 3dx3 + -1dx3y + -4dy2 = 0

Solving
2dx + 2dxy + -2dxy2 + 3dx3 + -1dx3y + -4dy2 = 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(2x + 2xy + -2xy2 + 3x3 + -1x3y + -4y2) = 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 '(2x + 2xy + -2xy2 + 3x3 + -1x3y + -4y2)' equal to zero and attempt to solve: Simplifying 2x + 2xy + -2xy2 + 3x3 + -1x3y + -4y2 = 0 Solving 2x + 2xy + -2xy2 + 3x3 + -1x3y + -4y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + 2xy + -2xy2 + 3x3 + -1x3y + -2x + -4y2 = 0 + -2x Reorder the terms: 2x + -2x + 2xy + -2xy2 + 3x3 + -1x3y + -4y2 = 0 + -2x Combine like terms: 2x + -2x = 0 0 + 2xy + -2xy2 + 3x3 + -1x3y + -4y2 = 0 + -2x 2xy + -2xy2 + 3x3 + -1x3y + -4y2 = 0 + -2x Remove the zero: 2xy + -2xy2 + 3x3 + -1x3y + -4y2 = -2x Add '-2xy' to each side of the equation. 2xy + -2xy2 + 3x3 + -1x3y + -2xy + -4y2 = -2x + -2xy Reorder the terms: 2xy + -2xy + -2xy2 + 3x3 + -1x3y + -4y2 = -2x + -2xy Combine like terms: 2xy + -2xy = 0 0 + -2xy2 + 3x3 + -1x3y + -4y2 = -2x + -2xy -2xy2 + 3x3 + -1x3y + -4y2 = -2x + -2xy Add '2xy2' to each side of the equation. -2xy2 + 3x3 + -1x3y + 2xy2 + -4y2 = -2x + -2xy + 2xy2 Reorder the terms: -2xy2 + 2xy2 + 3x3 + -1x3y + -4y2 = -2x + -2xy + 2xy2 Combine like terms: -2xy2 + 2xy2 = 0 0 + 3x3 + -1x3y + -4y2 = -2x + -2xy + 2xy2 3x3 + -1x3y + -4y2 = -2x + -2xy + 2xy2 Add '-3x3' to each side of the equation. 3x3 + -1x3y + -3x3 + -4y2 = -2x + -2xy + 2xy2 + -3x3 Reorder the terms: 3x3 + -3x3 + -1x3y + -4y2 = -2x + -2xy + 2xy2 + -3x3 Combine like terms: 3x3 + -3x3 = 0 0 + -1x3y + -4y2 = -2x + -2xy + 2xy2 + -3x3 -1x3y + -4y2 = -2x + -2xy + 2xy2 + -3x3 Add 'x3y' to each side of the equation. -1x3y + x3y + -4y2 = -2x + -2xy + 2xy2 + -3x3 + x3y Combine like terms: -1x3y + x3y = 0 0 + -4y2 = -2x + -2xy + 2xy2 + -3x3 + x3y -4y2 = -2x + -2xy + 2xy2 + -3x3 + x3y Add '4y2' to each side of the equation. -4y2 + 4y2 = -2x + -2xy + 2xy2 + -3x3 + x3y + 4y2 Combine like terms: -4y2 + 4y2 = 0 0 = -2x + -2xy + 2xy2 + -3x3 + x3y + 4y2 Simplifying 0 = -2x + -2xy + 2xy2 + -3x3 + x3y + 4y2 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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