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

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


Simplifying
(x2 + y2) * dx = (xy + -1x2) * dy

Reorder the terms for easier multiplication:
dx(x2 + y2) = (xy + -1x2) * dy
(x2 * dx + y2 * dx) = (xy + -1x2) * dy

Reorder the terms:
(dxy2 + dx3) = (xy + -1x2) * dy
(dxy2 + dx3) = (xy + -1x2) * dy

Reorder the terms for easier multiplication:
dxy2 + dx3 = dy(xy + -1x2)
dxy2 + dx3 = (xy * dy + -1x2 * dy)
dxy2 + dx3 = (dxy2 + -1dx2y)

Add '-1dxy2' to each side of the equation.
dxy2 + -1dxy2 + dx3 = dxy2 + -1dxy2 + -1dx2y

Combine like terms: dxy2 + -1dxy2 = 0
0 + dx3 = dxy2 + -1dxy2 + -1dx2y
dx3 = dxy2 + -1dxy2 + -1dx2y

Combine like terms: dxy2 + -1dxy2 = 0
dx3 = 0 + -1dx2y
dx3 = -1dx2y

Solving
dx3 = -1dx2y

Solving for variable 'd'.

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

Add 'dx2y' to each side of the equation.
dx2y + dx3 = -1dx2y + dx2y

Combine like terms: -1dx2y + dx2y = 0
dx2y + dx3 = 0

Factor out the Greatest Common Factor (GCF), 'dx2'.
dx2(y + x) = 0


Subproblem 1
Set the factor 'dx2' equal to zero and attempt to solve:

Simplifying
dx2 = 0

Solving
dx2 = 0

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

Simplifying
dx2 = 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 '(y + x)' equal to zero and attempt to solve:

Simplifying
y + x = 0

Reorder the terms:
x + y = 0

Solving
x + y = 0

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

Add '-1x' to each side of the equation.
x + -1x + y = 0 + -1x

Combine like terms: x + -1x = 0
0 + y = 0 + -1x
y = 0 + -1x
Remove the zero:
y = -1x

Add '-1y' to each side of the equation.
y + -1y = -1x + -1y

Combine like terms: y + -1y = 0
0 = -1x + -1y

Simplifying
0 = -1x + -1y

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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