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

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


Simplifying
x2dy + y(x + y) * dx = 0

Reorder the terms for easier multiplication:
dx2y + y * dx(x + y) = 0

Multiply y * dx
dx2y + dxy(x + y) = 0
dx2y + (x * dxy + y * dxy) = 0

Reorder the terms:
dx2y + (dxy2 + dx2y) = 0
dx2y + (dxy2 + dx2y) = 0

Reorder the terms:
dxy2 + dx2y + dx2y = 0

Combine like terms: dx2y + dx2y = 2dx2y
dxy2 + 2dx2y = 0

Solving
dxy2 + 2dx2y = 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(y + 2x) = 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 '(y + 2x)' equal to zero and attempt to solve:

Simplifying
y + 2x = 0

Reorder the terms:
2x + y = 0

Solving
2x + y = 0

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

Add '-2x' to each side of the equation.
2x + -2x + y = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + y = 0 + -2x
y = 0 + -2x
Remove the zero:
y = -2x

Add '-1y' to each side of the equation.
y + -1y = -2x + -1y

Combine like terms: y + -1y = 0
0 = -2x + -1y

Simplifying
0 = -2x + -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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