(x^3+x^2+y)dx+(1+x)dy=0

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Solution for (x^3+x^2+y)dx+(1+x)dy=0 equation: 


Simplifying
(x3 + x2 + y) * dx + (1 + x) * dy = 0

Reorder the terms:
(x2 + x3 + y) * dx + (1 + x) * dy = 0

Reorder the terms for easier multiplication:
dx(x2 + x3 + y) + (1 + x) * dy = 0
(x2 * dx + x3 * dx + y * dx) + (1 + x) * dy = 0

Reorder the terms:
(dxy + dx3 + dx4) + (1 + x) * dy = 0
(dxy + dx3 + dx4) + (1 + x) * dy = 0

Reorder the terms for easier multiplication:
dxy + dx3 + dx4 + dy(1 + x) = 0
dxy + dx3 + dx4 + (1 * dy + x * dy) = 0

Reorder the terms:
dxy + dx3 + dx4 + (dxy + 1dy) = 0
dxy + dx3 + dx4 + (dxy + 1dy) = 0

Reorder the terms:
dxy + dxy + dx3 + dx4 + 1dy = 0

Combine like terms: dxy + dxy = 2dxy
2dxy + dx3 + dx4 + 1dy = 0

Solving
2dxy + dx3 + dx4 + 1dy = 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(2xy + x3 + x4 + y) = 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 '(2xy + x3 + x4 + y)' equal to zero and attempt to solve:

Simplifying
2xy + x3 + x4 + y = 0

Solving
2xy + x3 + x4 + y = 0

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

Add '-2xy' to each side of the equation.
2xy + x3 + x4 + -2xy + y = 0 + -2xy

Reorder the terms:
2xy + -2xy + x3 + x4 + y = 0 + -2xy

Combine like terms: 2xy + -2xy = 0
0 + x3 + x4 + y = 0 + -2xy
x3 + x4 + y = 0 + -2xy
Remove the zero:
x3 + x4 + y = -2xy

Add '-1x3' to each side of the equation.
x3 + x4 + -1x3 + y = -2xy + -1x3

Reorder the terms:
x3 + -1x3 + x4 + y = -2xy + -1x3

Combine like terms: x3 + -1x3 = 0
0 + x4 + y = -2xy + -1x3
x4 + y = -2xy + -1x3

Add '-1x4' to each side of the equation.
x4 + -1x4 + y = -2xy + -1x3 + -1x4

Combine like terms: x4 + -1x4 = 0
0 + y = -2xy + -1x3 + -1x4
y = -2xy + -1x3 + -1x4

Add '-1y' to each side of the equation.
y + -1y = -2xy + -1x3 + -1x4 + -1y

Combine like terms: y + -1y = 0
0 = -2xy + -1x3 + -1x4 + -1y

Simplifying
0 = -2xy + -1x3 + -1x4 + -1y

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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