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

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


Simplifying
(2x) * dx + (y2 + -1x2) * dy = 0

Remove parenthesis around (2x)
2x * dx + (y2 + -1x2) * dy = 0

Multiply x * dx
2dx2 + (y2 + -1x2) * dy = 0

Reorder the terms:
2dx2 + (-1x2 + y2) * dy = 0

Reorder the terms for easier multiplication:
2dx2 + dy(-1x2 + y2) = 0
2dx2 + (-1x2 * dy + y2 * dy) = 0
2dx2 + (-1dx2y + dy3) = 0

Solving
2dx2 + -1dx2y + dy3 = 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(2x2 + -1x2y + y3) = 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 '(2x2 + -1x2y + y3)' equal to zero and attempt to solve:

Simplifying
2x2 + -1x2y + y3 = 0

Solving
2x2 + -1x2y + y3 = 0

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

Add '-2x2' to each side of the equation.
2x2 + -1x2y + -2x2 + y3 = 0 + -2x2

Reorder the terms:
2x2 + -2x2 + -1x2y + y3 = 0 + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + -1x2y + y3 = 0 + -2x2
-1x2y + y3 = 0 + -2x2
Remove the zero:
-1x2y + y3 = -2x2

Add 'x2y' to each side of the equation.
-1x2y + x2y + y3 = -2x2 + x2y

Combine like terms: -1x2y + x2y = 0
0 + y3 = -2x2 + x2y
y3 = -2x2 + x2y

Add '-1y3' to each side of the equation.
y3 + -1y3 = -2x2 + x2y + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -2x2 + x2y + -1y3

Simplifying
0 = -2x2 + x2y + -1y3

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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