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

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


Simplifying
(x2 + y2) * dy + (2xy) * dx = 0

Reorder the terms for easier multiplication:
dy(x2 + y2) + (2xy) * dx = 0
(x2 * dy + y2 * dy) + (2xy) * dx = 0
(dx2y + dy3) + (2xy) * dx = 0

Remove parenthesis around (2xy)
dx2y + dy3 + 2xy * dx = 0

Multiply xy * dx
dx2y + dy3 + 2dx2y = 0

Reorder the terms:
dx2y + 2dx2y + dy3 = 0

Combine like terms: dx2y + 2dx2y = 3dx2y
3dx2y + dy3 = 0

Solving
3dx2y + 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), 'dy'.
dy(3x2 + y2) = 0


Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve:

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(3x2 + y2)' equal to zero and attempt to solve:

Simplifying
3x2 + y2 = 0

Solving
3x2 + y2 = 0

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

Add '-3x2' to each side of the equation.
3x2 + -3x2 + y2 = 0 + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + y2 = 0 + -3x2
y2 = 0 + -3x2
Remove the zero:
y2 = -3x2

Add '-1y2' to each side of the equation.
y2 + -1y2 = -3x2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -3x2 + -1y2

Simplifying
0 = -3x2 + -1y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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