(3x-2y+1)dx+(3x-2y-3)dy=0

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Solution for (3x-2y+1)dx+(3x-2y-3)dy=0 equation:


Simplifying
(3x + -2y + 1) * dx + (3x + -2y + -3) * dy = 0

Reorder the terms:
(1 + 3x + -2y) * dx + (3x + -2y + -3) * dy = 0

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

Reorder the terms:
(1dx + -2dxy + 3dx2) + (3x + -2y + -3) * dy = 0
(1dx + -2dxy + 3dx2) + (3x + -2y + -3) * dy = 0

Reorder the terms:
1dx + -2dxy + 3dx2 + (-3 + 3x + -2y) * dy = 0

Reorder the terms for easier multiplication:
1dx + -2dxy + 3dx2 + dy(-3 + 3x + -2y) = 0
1dx + -2dxy + 3dx2 + (-3 * dy + 3x * dy + -2y * dy) = 0

Reorder the terms:
1dx + -2dxy + 3dx2 + (3dxy + -3dy + -2dy2) = 0
1dx + -2dxy + 3dx2 + (3dxy + -3dy + -2dy2) = 0

Reorder the terms:
1dx + -2dxy + 3dxy + 3dx2 + -3dy + -2dy2 = 0

Combine like terms: -2dxy + 3dxy = 1dxy
1dx + 1dxy + 3dx2 + -3dy + -2dy2 = 0

Solving
1dx + 1dxy + 3dx2 + -3dy + -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(x + xy + 3x2 + -3y + -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 '(x + xy + 3x2 + -3y + -2y2)' equal to zero and attempt to solve: Simplifying x + xy + 3x2 + -3y + -2y2 = 0 Solving x + xy + 3x2 + -3y + -2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + xy + 3x2 + -3y + -1x + -2y2 = 0 + -1x Reorder the terms: x + -1x + xy + 3x2 + -3y + -2y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + xy + 3x2 + -3y + -2y2 = 0 + -1x xy + 3x2 + -3y + -2y2 = 0 + -1x Remove the zero: xy + 3x2 + -3y + -2y2 = -1x Add '-1xy' to each side of the equation. xy + 3x2 + -3y + -1xy + -2y2 = -1x + -1xy Reorder the terms: xy + -1xy + 3x2 + -3y + -2y2 = -1x + -1xy Combine like terms: xy + -1xy = 0 0 + 3x2 + -3y + -2y2 = -1x + -1xy 3x2 + -3y + -2y2 = -1x + -1xy Add '-3x2' to each side of the equation. 3x2 + -3y + -3x2 + -2y2 = -1x + -1xy + -3x2 Reorder the terms: 3x2 + -3x2 + -3y + -2y2 = -1x + -1xy + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 + -3y + -2y2 = -1x + -1xy + -3x2 -3y + -2y2 = -1x + -1xy + -3x2 Add '3y' to each side of the equation. -3y + 3y + -2y2 = -1x + -1xy + -3x2 + 3y Combine like terms: -3y + 3y = 0 0 + -2y2 = -1x + -1xy + -3x2 + 3y -2y2 = -1x + -1xy + -3x2 + 3y Add '2y2' to each side of the equation. -2y2 + 2y2 = -1x + -1xy + -3x2 + 3y + 2y2 Combine like terms: -2y2 + 2y2 = 0 0 = -1x + -1xy + -3x2 + 3y + 2y2 Simplifying 0 = -1x + -1xy + -3x2 + 3y + 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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