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

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


Simplifying
(y + x + (y2)) * dx + -1xdy = 0
(y + x + y2) * dx + -1xdy = 0

Reorder the terms:
(x + y + y2) * dx + -1xdy = 0

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

Reorder the terms:
(dxy + dxy2 + dx2) + -1xdy = 0
(dxy + dxy2 + dx2) + -1xdy = 0

Reorder the terms:
dxy + -1dxy + dxy2 + dx2 = 0

Combine like terms: dxy + -1dxy = 0
0 + dxy2 + dx2 = 0
dxy2 + dx2 = 0

Solving
dxy2 + dx2 = 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), 'dx'.
dx(y2 + x) = 0


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

Simplifying
dx = 0

Solving
dx = 0

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

Simplifying
dx = 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 + x)' equal to zero and attempt to solve:

Simplifying
y2 + x = 0

Reorder the terms:
x + y2 = 0

Solving
x + y2 = 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 + y2 = 0 + -1x

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

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

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

Simplifying
0 = -1x + -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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