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

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


Simplifying
(X2 + -1y) * dx + (x + -1y2) * dy = 0

Reorder the terms for easier multiplication:
dx(X2 + -1y) + (x + -1y2) * dy = 0
(X2 * dx + -1y * dx) + (x + -1y2) * dy = 0
(dxX2 + -1dxy) + (x + -1y2) * dy = 0

Reorder the terms for easier multiplication:
dxX2 + -1dxy + dy(x + -1y2) = 0
dxX2 + -1dxy + (x * dy + -1y2 * dy) = 0
dxX2 + -1dxy + (dxy + -1dy3) = 0

Combine like terms: -1dxy + dxy = 0
dxX2 + 0 + -1dy3 = 0
dxX2 + -1dy3 = 0

Solving
dxX2 + -1dy3 = 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(xX2 + -1y3) = 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 '(xX2 + -1y3)' equal to zero and attempt to solve:

Simplifying
xX2 + -1y3 = 0

Solving
xX2 + -1y3 = 0

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

Add '-1xX2' to each side of the equation.
xX2 + -1xX2 + -1y3 = 0 + -1xX2

Combine like terms: xX2 + -1xX2 = 0
0 + -1y3 = 0 + -1xX2
-1y3 = 0 + -1xX2
Remove the zero:
-1y3 = -1xX2

Add 'y3' to each side of the equation.
-1y3 + y3 = -1xX2 + y3

Combine like terms: -1y3 + y3 = 0
0 = -1xX2 + y3

Simplifying
0 = -1xX2 + y3

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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