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

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


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

Reorder the terms for easier multiplication:
x * dx(x + 2y) + (x2 + -1y2) * dy = 0

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

Reorder the terms:
(2dx2y + dx3) + (x2 + -1y2) * dy = 0
(2dx2y + dx3) + (x2 + -1y2) * dy = 0

Reorder the terms for easier multiplication:
2dx2y + dx3 + dy(x2 + -1y2) = 0
2dx2y + dx3 + (x2 * dy + -1y2 * dy) = 0
2dx2y + dx3 + (dx2y + -1dy3) = 0

Reorder the terms:
2dx2y + dx2y + dx3 + -1dy3 = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
3dx2y + dx3 + -1dy3 = 0

Solving
3dx2y + dx3 + -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(3x2y + x3 + -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 '(3x2y + x3 + -1y3)' equal to zero and attempt to solve:

Simplifying
3x2y + x3 + -1y3 = 0

Solving
3x2y + x3 + -1y3 = 0

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

Add '-3x2y' to each side of the equation.
3x2y + x3 + -3x2y + -1y3 = 0 + -3x2y

Reorder the terms:
3x2y + -3x2y + x3 + -1y3 = 0 + -3x2y

Combine like terms: 3x2y + -3x2y = 0
0 + x3 + -1y3 = 0 + -3x2y
x3 + -1y3 = 0 + -3x2y
Remove the zero:
x3 + -1y3 = -3x2y

Add '-1x3' to each side of the equation.
x3 + -1x3 + -1y3 = -3x2y + -1x3

Combine like terms: x3 + -1x3 = 0
0 + -1y3 = -3x2y + -1x3
-1y3 = -3x2y + -1x3

Add 'y3' to each side of the equation.
-1y3 + y3 = -3x2y + -1x3 + y3

Combine like terms: -1y3 + y3 = 0
0 = -3x2y + -1x3 + y3

Simplifying
0 = -3x2y + -1x3 + 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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