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

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


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

Reorder the terms for easier multiplication:
y2 + dy(xy + x2) = 0
y2 + (xy * dy + x2 * dy) = 0
y2 + (dxy2 + dx2y) = 0

Reorder the terms:
dxy2 + dx2y + y2 = 0

Solving
dxy2 + dx2y + y2 = 0

Solving for variable 'd'.

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

Add '-1y2' to each side of the equation.
dxy2 + dx2y + y2 + -1y2 = 0 + -1y2

Combine like terms: y2 + -1y2 = 0
dxy2 + dx2y + 0 = 0 + -1y2
dxy2 + dx2y = 0 + -1y2
Remove the zero:
dxy2 + dx2y = -1y2

Combine like terms: -1y2 + y2 = 0
dxy2 + dx2y + y2 = 0

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


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

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

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 '(dxy + dx2 + y)' equal to zero and attempt to solve:

Simplifying
dxy + dx2 + y = 0

Solving
dxy + dx2 + y = 0

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

Add '-1y' to each side of the equation.
dxy + dx2 + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
dxy + dx2 + 0 = 0 + -1y
dxy + dx2 = 0 + -1y
Remove the zero:
dxy + dx2 = -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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