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

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


Simplifying
(2x + 6x2y) * dx + (3x3 + -2xy) * dy = 0

Reorder the terms for easier multiplication:
dx(2x + 6x2y) + (3x3 + -2xy) * dy = 0
(2x * dx + 6x2y * dx) + (3x3 + -2xy) * dy = 0
(2dx2 + 6dx3y) + (3x3 + -2xy) * dy = 0

Reorder the terms:
2dx2 + 6dx3y + (-2xy + 3x3) * dy = 0

Reorder the terms for easier multiplication:
2dx2 + 6dx3y + dy(-2xy + 3x3) = 0
2dx2 + 6dx3y + (-2xy * dy + 3x3 * dy) = 0
2dx2 + 6dx3y + (-2dxy2 + 3dx3y) = 0

Reorder the terms:
-2dxy2 + 2dx2 + 6dx3y + 3dx3y = 0

Combine like terms: 6dx3y + 3dx3y = 9dx3y
-2dxy2 + 2dx2 + 9dx3y = 0

Solving
-2dxy2 + 2dx2 + 9dx3y = 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(-2y2 + 2x + 9x2y) = 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 '(-2y2 + 2x + 9x2y)' equal to zero and attempt to solve: Simplifying -2y2 + 2x + 9x2y = 0 Reorder the terms: 2x + 9x2y + -2y2 = 0 Solving 2x + 9x2y + -2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + 9x2y + -2x + -2y2 = 0 + -2x Reorder the terms: 2x + -2x + 9x2y + -2y2 = 0 + -2x Combine like terms: 2x + -2x = 0 0 + 9x2y + -2y2 = 0 + -2x 9x2y + -2y2 = 0 + -2x Remove the zero: 9x2y + -2y2 = -2x Add '-9x2y' to each side of the equation. 9x2y + -9x2y + -2y2 = -2x + -9x2y Combine like terms: 9x2y + -9x2y = 0 0 + -2y2 = -2x + -9x2y -2y2 = -2x + -9x2y Add '2y2' to each side of the equation. -2y2 + 2y2 = -2x + -9x2y + 2y2 Combine like terms: -2y2 + 2y2 = 0 0 = -2x + -9x2y + 2y2 Simplifying 0 = -2x + -9x2y + 2y2 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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