(2x+4y)DX+(2x+2y)dy=0

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Solution for (2x+4y)DX+(2x+2y)dy=0 equation: 


Simplifying
(2x + 4y) * DX + (2x + 2y) * dy = 0

Reorder the terms for easier multiplication:
DX(2x + 4y) + (2x + 2y) * dy = 0
(2x * DX + 4y * DX) + (2x + 2y) * dy = 0
(2xDX + 4yDX) + (2x + 2y) * dy = 0

Reorder the terms for easier multiplication:
2xDX + 4yDX + dy(2x + 2y) = 0
2xDX + 4yDX + (2x * dy + 2y * dy) = 0
2xDX + 4yDX + (2dxy + 2dy2) = 0

Reorder the terms:
2dxy + 2dy2 + 2xDX + 4yDX = 0

Solving
2dxy + 2dy2 + 2xDX + 4yDX = 0

Solving for variable 'd'.

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

Add '-2xDX' to each side of the equation.
2dxy + 2dy2 + 2xDX + -2xDX + 4yDX = 0 + -2xDX

Combine like terms: 2xDX + -2xDX = 0
2dxy + 2dy2 + 0 + 4yDX = 0 + -2xDX
2dxy + 2dy2 + 4yDX = 0 + -2xDX
Remove the zero:
2dxy + 2dy2 + 4yDX = -2xDX

Add '-4yDX' to each side of the equation.
2dxy + 2dy2 + 4yDX + -4yDX = -2xDX + -4yDX

Combine like terms: 4yDX + -4yDX = 0
2dxy + 2dy2 + 0 = -2xDX + -4yDX
2dxy + 2dy2 = -2xDX + -4yDX

Reorder the terms:
2dxy + 2dy2 + 2xDX + 4yDX = -2xDX + 2xDX + -4yDX + 4yDX

Combine like terms: -2xDX + 2xDX = 0
2dxy + 2dy2 + 2xDX + 4yDX = 0 + -4yDX + 4yDX
2dxy + 2dy2 + 2xDX + 4yDX = -4yDX + 4yDX

Combine like terms: -4yDX + 4yDX = 0
2dxy + 2dy2 + 2xDX + 4yDX = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(dxy + dy2 + xDX + 2yDX) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(dxy + dy2 + xDX + 2yDX)' equal to zero and attempt to solve:

Simplifying
dxy + dy2 + xDX + 2yDX = 0

Solving
dxy + dy2 + xDX + 2yDX = 0

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

Add '-1xDX' to each side of the equation.
dxy + dy2 + xDX + -1xDX + 2yDX = 0 + -1xDX

Combine like terms: xDX + -1xDX = 0
dxy + dy2 + 0 + 2yDX = 0 + -1xDX
dxy + dy2 + 2yDX = 0 + -1xDX
Remove the zero:
dxy + dy2 + 2yDX = -1xDX

Add '-2yDX' to each side of the equation.
dxy + dy2 + 2yDX + -2yDX = -1xDX + -2yDX

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

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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