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

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


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

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

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

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

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

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

Solving
1dxy + -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), 'dy'.
dy(x + -2y) = 0


Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve:

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 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 '(x + -2y)' equal to zero and attempt to solve:

Simplifying
x + -2y = 0

Solving
x + -2y = 0

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

Add '-1x' to each side of the equation.
x + -1x + -2y = 0 + -1x

Combine like terms: x + -1x = 0
0 + -2y = 0 + -1x
-2y = 0 + -1x
Remove the zero:
-2y = -1x

Add '2y' to each side of the equation.
-2y + 2y = -1x + 2y

Combine like terms: -2y + 2y = 0
0 = -1x + 2y

Simplifying
0 = -1x + 2y

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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