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

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


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

Reorder the terms for easier multiplication:
dy(2x + y) + -1(3x + -2y) * dx = 0
(2x * dy + y * dy) + -1(3x + -2y) * dx = 0
(2dxy + dy2) + -1(3x + -2y) * dx = 0

Reorder the terms for easier multiplication:
2dxy + dy2 + -1dx(3x + -2y) = 0
2dxy + dy2 + (3x * -1dx + -2y * -1dx) = 0

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

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

Combine like terms: 2dxy + 2dxy = 4dxy
4dxy + -3dx2 + dy2 = 0

Solving
4dxy + -3dx2 + dy2 = 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(4xy + -3x2 + y2) = 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 '(4xy + -3x2 + y2)' equal to zero and attempt to solve:

Simplifying
4xy + -3x2 + y2 = 0

Solving
4xy + -3x2 + y2 = 0

Move all terms containing d to the left, all other terms to the right.

Add '-4xy' to each side of the equation.
4xy + -3x2 + -4xy + y2 = 0 + -4xy

Reorder the terms:
4xy + -4xy + -3x2 + y2 = 0 + -4xy

Combine like terms: 4xy + -4xy = 0
0 + -3x2 + y2 = 0 + -4xy
-3x2 + y2 = 0 + -4xy
Remove the zero:
-3x2 + y2 = -4xy

Add '3x2' to each side of the equation.
-3x2 + 3x2 + y2 = -4xy + 3x2

Combine like terms: -3x2 + 3x2 = 0
0 + y2 = -4xy + 3x2
y2 = -4xy + 3x2

Add '-1y2' to each side of the equation.
y2 + -1y2 = -4xy + 3x2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -4xy + 3x2 + -1y2

Simplifying
0 = -4xy + 3x2 + -1y2

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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