(x-2y+5)dx+(2x-y+4)dy=0

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Solution for (x-2y+5)dx+(2x-y+4)dy=0 equation: 


Simplifying
(x + -2y + 5) * dx + (2x + -1y + 4) * dy = 0

Reorder the terms:
(5 + x + -2y) * dx + (2x + -1y + 4) * dy = 0

Reorder the terms for easier multiplication:
dx(5 + x + -2y) + (2x + -1y + 4) * dy = 0
(5 * dx + x * dx + -2y * dx) + (2x + -1y + 4) * dy = 0

Reorder the terms:
(5dx + -2dxy + dx2) + (2x + -1y + 4) * dy = 0
(5dx + -2dxy + dx2) + (2x + -1y + 4) * dy = 0

Reorder the terms:
5dx + -2dxy + dx2 + (4 + 2x + -1y) * dy = 0

Reorder the terms for easier multiplication:
5dx + -2dxy + dx2 + dy(4 + 2x + -1y) = 0
5dx + -2dxy + dx2 + (4 * dy + 2x * dy + -1y * dy) = 0

Reorder the terms:
5dx + -2dxy + dx2 + (2dxy + 4dy + -1dy2) = 0
5dx + -2dxy + dx2 + (2dxy + 4dy + -1dy2) = 0

Reorder the terms:
5dx + -2dxy + 2dxy + dx2 + 4dy + -1dy2 = 0

Combine like terms: -2dxy + 2dxy = 0
5dx + 0 + dx2 + 4dy + -1dy2 = 0
5dx + dx2 + 4dy + -1dy2 = 0

Solving
5dx + dx2 + 4dy + -1dy2 = 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(5x + x2 + 4y + -1y2) = 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 '(5x + x2 + 4y + -1y2)' equal to zero and attempt to solve:

Simplifying
5x + x2 + 4y + -1y2 = 0

Solving
5x + x2 + 4y + -1y2 = 0

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

Add '-5x' to each side of the equation.
5x + x2 + 4y + -5x + -1y2 = 0 + -5x

Reorder the terms:
5x + -5x + x2 + 4y + -1y2 = 0 + -5x

Combine like terms: 5x + -5x = 0
0 + x2 + 4y + -1y2 = 0 + -5x
x2 + 4y + -1y2 = 0 + -5x
Remove the zero:
x2 + 4y + -1y2 = -5x

Add '-1x2' to each side of the equation.
x2 + 4y + -1x2 + -1y2 = -5x + -1x2

Reorder the terms:
x2 + -1x2 + 4y + -1y2 = -5x + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 4y + -1y2 = -5x + -1x2
4y + -1y2 = -5x + -1x2

Add '-4y' to each side of the equation.
4y + -4y + -1y2 = -5x + -1x2 + -4y

Combine like terms: 4y + -4y = 0
0 + -1y2 = -5x + -1x2 + -4y
-1y2 = -5x + -1x2 + -4y

Add 'y2' to each side of the equation.
-1y2 + y2 = -5x + -1x2 + -4y + y2

Combine like terms: -1y2 + y2 = 0
0 = -5x + -1x2 + -4y + y2

Simplifying
0 = -5x + -1x2 + -4y + y2

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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