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

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Solution for (5x-y+2)dx+(2x-y+1)dy=0 equation: 


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

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

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

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

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

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

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

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

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

Solving
2dx + 1dxy + 5dx2 + 1dy + -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(2x + xy + 5x2 + y + -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 '(2x + xy + 5x2 + y + -1y2)' equal to zero and attempt to solve:

Simplifying
2x + xy + 5x2 + y + -1y2 = 0

Solving
2x + xy + 5x2 + y + -1y2 = 0

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

Add '-2x' to each side of the equation.
2x + xy + 5x2 + y + -2x + -1y2 = 0 + -2x

Reorder the terms:
2x + -2x + xy + 5x2 + y + -1y2 = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + xy + 5x2 + y + -1y2 = 0 + -2x
xy + 5x2 + y + -1y2 = 0 + -2x
Remove the zero:
xy + 5x2 + y + -1y2 = -2x

Add '-1xy' to each side of the equation.
xy + 5x2 + y + -1xy + -1y2 = -2x + -1xy

Reorder the terms:
xy + -1xy + 5x2 + y + -1y2 = -2x + -1xy

Combine like terms: xy + -1xy = 0
0 + 5x2 + y + -1y2 = -2x + -1xy
5x2 + y + -1y2 = -2x + -1xy

Add '-5x2' to each side of the equation.
5x2 + y + -5x2 + -1y2 = -2x + -1xy + -5x2

Reorder the terms:
5x2 + -5x2 + y + -1y2 = -2x + -1xy + -5x2

Combine like terms: 5x2 + -5x2 = 0
0 + y + -1y2 = -2x + -1xy + -5x2
y + -1y2 = -2x + -1xy + -5x2

Add '-1y' to each side of the equation.
y + -1y + -1y2 = -2x + -1xy + -5x2 + -1y

Combine like terms: y + -1y = 0
0 + -1y2 = -2x + -1xy + -5x2 + -1y
-1y2 = -2x + -1xy + -5x2 + -1y

Add 'y2' to each side of the equation.
-1y2 + y2 = -2x + -1xy + -5x2 + -1y + y2

Combine like terms: -1y2 + y2 = 0
0 = -2x + -1xy + -5x2 + -1y + y2

Simplifying
0 = -2x + -1xy + -5x2 + -1y + 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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