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

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


Simplifying
(xy2 + x) * dy + (x2y + -1y) * dx = 0

Reorder the terms:
(x + xy2) * dy + (x2y + -1y) * dx = 0

Reorder the terms for easier multiplication:
dy(x + xy2) + (x2y + -1y) * dx = 0
(x * dy + xy2 * dy) + (x2y + -1y) * dx = 0
(dxy + dxy3) + (x2y + -1y) * dx = 0

Reorder the terms for easier multiplication:
dxy + dxy3 + dx(x2y + -1y) = 0
dxy + dxy3 + (x2y * dx + -1y * dx) = 0

Reorder the terms:
dxy + dxy3 + (-1dxy + dx3y) = 0
dxy + dxy3 + (-1dxy + dx3y) = 0

Reorder the terms:
dxy + -1dxy + dxy3 + dx3y = 0

Combine like terms: dxy + -1dxy = 0
0 + dxy3 + dx3y = 0
dxy3 + dx3y = 0

Solving
dxy3 + dx3y = 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), 'dxy'.
dxy(y2 + x2) = 0


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

Simplifying
dxy = 0

Solving
dxy = 0

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

Simplifying
dxy = 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 '(y2 + x2)' equal to zero and attempt to solve:

Simplifying
y2 + x2 = 0

Reorder the terms:
x2 + y2 = 0

Solving
x2 + y2 = 0

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

Add '-1x2' to each side of the equation.
x2 + -1x2 + y2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + y2 = 0 + -1x2
y2 = 0 + -1x2
Remove the zero:
y2 = -1x2

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

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

Simplifying
0 = -1x2 + -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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