Xdy-(x+2*y^2)dx=0

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Solution for Xdy-(x+2*y^2)dx=0 equation: 


Simplifying
Xdy + -1(x + 2y2) * dx = 0

Reorder the terms for easier multiplication:
dyX + -1dx(x + 2y2) = 0
dyX + (x * -1dx + 2y2 * -1dx) = 0

Reorder the terms:
dyX + (-2dxy2 + -1dx2) = 0
dyX + (-2dxy2 + -1dx2) = 0

Reorder the terms:
-2dxy2 + -1dx2 + dyX = 0

Solving
-2dxy2 + -1dx2 + dyX = 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(-2xy2 + -1x2 + yX) = 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 '(-2xy2 + -1x2 + yX)' equal to zero and attempt to solve:

Simplifying
-2xy2 + -1x2 + yX = 0

Solving
-2xy2 + -1x2 + yX = 0

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

Add '2xy2' to each side of the equation.
-2xy2 + -1x2 + 2xy2 + yX = 0 + 2xy2

Reorder the terms:
-2xy2 + 2xy2 + -1x2 + yX = 0 + 2xy2

Combine like terms: -2xy2 + 2xy2 = 0
0 + -1x2 + yX = 0 + 2xy2
-1x2 + yX = 0 + 2xy2
Remove the zero:
-1x2 + yX = 2xy2

Add 'x2' to each side of the equation.
-1x2 + x2 + yX = 2xy2 + x2

Combine like terms: -1x2 + x2 = 0
0 + yX = 2xy2 + x2
yX = 2xy2 + x2

Add '-1yX' to each side of the equation.
yX + -1yX = 2xy2 + x2 + -1yX

Combine like terms: yX + -1yX = 0
0 = 2xy2 + x2 + -1yX

Simplifying
0 = 2xy2 + x2 + -1yX

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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