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

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


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

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

Reorder the terms:
(dxy2 + dx3) + (y2 + -1xy) * dy = 0
(dxy2 + dx3) + (y2 + -1xy) * dy = 0

Reorder the terms:
dxy2 + dx3 + (-1xy + y2) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + dx3 + dy(-1xy + y2) = 0
dxy2 + dx3 + (-1xy * dy + y2 * dy) = 0
dxy2 + dx3 + (-1dxy2 + dy3) = 0

Reorder the terms:
dxy2 + -1dxy2 + dx3 + dy3 = 0

Combine like terms: dxy2 + -1dxy2 = 0
0 + dx3 + dy3 = 0
dx3 + dy3 = 0

Solving
dx3 + 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(x3 + 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 '(x3 + y3)' equal to zero and attempt to solve:

Simplifying
x3 + y3 = 0

Solving
x3 + y3 = 0

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

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

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

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

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

Simplifying
0 = -1x3 + -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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