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

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


Simplifying
(X + -1y2x) * dx + (y + -1x2y) * dy = 0

Reorder the terms for easier multiplication:
dx(X + -1xy2) + (y + -1x2y) * dy = 0
(X * dx + -1xy2 * dx) + (y + -1x2y) * dy = 0
(dxX + -1dx2y2) + (y + -1x2y) * dy = 0

Reorder the terms:
dxX + -1dx2y2 + (-1x2y + y) * dy = 0

Reorder the terms for easier multiplication:
dxX + -1dx2y2 + dy(-1x2y + y) = 0
dxX + -1dx2y2 + (-1x2y * dy + y * dy) = 0
dxX + -1dx2y2 + (-1dx2y2 + dy2) = 0

Combine like terms: -1dx2y2 + -1dx2y2 = -2dx2y2
dxX + -2dx2y2 + dy2 = 0

Solving
dxX + -2dx2y2 + dy2 = 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 + -2x2y2 + y2) = 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 + -2x2y2 + y2)' equal to zero and attempt to solve:

Simplifying
xX + -2x2y2 + y2 = 0

Solving
xX + -2x2y2 + y2 = 0

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

Add '-1xX' to each side of the equation.
xX + -2x2y2 + -1xX + y2 = 0 + -1xX

Reorder the terms:
xX + -1xX + -2x2y2 + y2 = 0 + -1xX

Combine like terms: xX + -1xX = 0
0 + -2x2y2 + y2 = 0 + -1xX
-2x2y2 + y2 = 0 + -1xX
Remove the zero:
-2x2y2 + y2 = -1xX

Add '2x2y2' to each side of the equation.
-2x2y2 + 2x2y2 + y2 = -1xX + 2x2y2

Combine like terms: -2x2y2 + 2x2y2 = 0
0 + y2 = -1xX + 2x2y2
y2 = -1xX + 2x2y2

Add '-1y2' to each side of the equation.
y2 + -1y2 = -1xX + 2x2y2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -1xX + 2x2y2 + -1y2

Simplifying
0 = -1xX + 2x2y2 + -1y2

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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