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

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


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

Reorder the terms for easier multiplication:
dx(4xy + 3x2) + (2y + 2x2) * dy = 0
(4xy * dx + 3x2 * dx) + (2y + 2x2) * dy = 0
(4dx2y + 3dx3) + (2y + 2x2) * dy = 0

Reorder the terms:
4dx2y + 3dx3 + (2x2 + 2y) * dy = 0

Reorder the terms for easier multiplication:
4dx2y + 3dx3 + dy(2x2 + 2y) = 0
4dx2y + 3dx3 + (2x2 * dy + 2y * dy) = 0
4dx2y + 3dx3 + (2dx2y + 2dy2) = 0

Reorder the terms:
4dx2y + 2dx2y + 3dx3 + 2dy2 = 0

Combine like terms: 4dx2y + 2dx2y = 6dx2y
6dx2y + 3dx3 + 2dy2 = 0

Solving
6dx2y + 3dx3 + 2dy2 = 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(6x2y + 3x3 + 2y2) = 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 '(6x2y + 3x3 + 2y2)' equal to zero and attempt to solve: Simplifying 6x2y + 3x3 + 2y2 = 0 Solving 6x2y + 3x3 + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-6x2y' to each side of the equation. 6x2y + 3x3 + -6x2y + 2y2 = 0 + -6x2y Reorder the terms: 6x2y + -6x2y + 3x3 + 2y2 = 0 + -6x2y Combine like terms: 6x2y + -6x2y = 0 0 + 3x3 + 2y2 = 0 + -6x2y 3x3 + 2y2 = 0 + -6x2y Remove the zero: 3x3 + 2y2 = -6x2y Add '-3x3' to each side of the equation. 3x3 + -3x3 + 2y2 = -6x2y + -3x3 Combine like terms: 3x3 + -3x3 = 0 0 + 2y2 = -6x2y + -3x3 2y2 = -6x2y + -3x3 Add '-2y2' to each side of the equation. 2y2 + -2y2 = -6x2y + -3x3 + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = -6x2y + -3x3 + -2y2 Simplifying 0 = -6x2y + -3x3 + -2y2 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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