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

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


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

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

Reorder the terms for easier multiplication:
dxX + -2dxy + -1dy(2x + 5y) = 0
dxX + -2dxy + (2x * -1dy + 5y * -1dy) = 0
dxX + -2dxy + (-2dxy + -5dy2) = 0

Combine like terms: -2dxy + -2dxy = -4dxy
dxX + -4dxy + -5dy2 = 0

Solving
dxX + -4dxy + -5dy2 = 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(xX + -4xy + -5y2) = 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 '(xX + -4xy + -5y2)' equal to zero and attempt to solve:

Simplifying
xX + -4xy + -5y2 = 0

Solving
xX + -4xy + -5y2 = 0

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

Add '-1xX' to each side of the equation.
xX + -4xy + -1xX + -5y2 = 0 + -1xX

Reorder the terms:
xX + -1xX + -4xy + -5y2 = 0 + -1xX

Combine like terms: xX + -1xX = 0
0 + -4xy + -5y2 = 0 + -1xX
-4xy + -5y2 = 0 + -1xX
Remove the zero:
-4xy + -5y2 = -1xX

Add '4xy' to each side of the equation.
-4xy + 4xy + -5y2 = -1xX + 4xy

Combine like terms: -4xy + 4xy = 0
0 + -5y2 = -1xX + 4xy
-5y2 = -1xX + 4xy

Add '5y2' to each side of the equation.
-5y2 + 5y2 = -1xX + 4xy + 5y2

Combine like terms: -5y2 + 5y2 = 0
0 = -1xX + 4xy + 5y2

Simplifying
0 = -1xX + 4xy + 5y2

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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