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

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


Simplifying
(y2 + x2) * dy + (2xy + x) * dx = 0

Reorder the terms:
(x2 + y2) * dy + (2xy + x) * dx = 0

Reorder the terms for easier multiplication:
dy(x2 + y2) + (2xy + x) * dx = 0
(x2 * dy + y2 * dy) + (2xy + x) * dx = 0
(dx2y + dy3) + (2xy + x) * dx = 0

Reorder the terms:
dx2y + dy3 + (x + 2xy) * dx = 0

Reorder the terms for easier multiplication:
dx2y + dy3 + dx(x + 2xy) = 0
dx2y + dy3 + (x * dx + 2xy * dx) = 0
dx2y + dy3 + (dx2 + 2dx2y) = 0

Reorder the terms:
dx2 + dx2y + 2dx2y + dy3 = 0

Combine like terms: dx2y + 2dx2y = 3dx2y
dx2 + 3dx2y + dy3 = 0

Solving
dx2 + 3dx2y + 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(x2 + 3x2y + 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 '(x2 + 3x2y + y3)' equal to zero and attempt to solve:

Simplifying
x2 + 3x2y + y3 = 0

Solving
x2 + 3x2y + y3 = 0

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

Add '-1x2' to each side of the equation.
x2 + 3x2y + -1x2 + y3 = 0 + -1x2

Reorder the terms:
x2 + -1x2 + 3x2y + y3 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 3x2y + y3 = 0 + -1x2
3x2y + y3 = 0 + -1x2
Remove the zero:
3x2y + y3 = -1x2

Add '-3x2y' to each side of the equation.
3x2y + -3x2y + y3 = -1x2 + -3x2y

Combine like terms: 3x2y + -3x2y = 0
0 + y3 = -1x2 + -3x2y
y3 = -1x2 + -3x2y

Add '-1y3' to each side of the equation.
y3 + -1y3 = -1x2 + -3x2y + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -1x2 + -3x2y + -1y3

Simplifying
0 = -1x2 + -3x2y + -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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