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

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


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

Multiply x2 * dx
dx3 + y(x + -1) * dy = 0

Reorder the terms:
dx3 + y(-1 + x) * dy = 0

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

Multiply y * dy
dx3 + dy2(-1 + x) = 0
dx3 + (-1 * dy2 + x * dy2) = 0

Reorder the terms:
dx3 + (dxy2 + -1dy2) = 0
dx3 + (dxy2 + -1dy2) = 0

Reorder the terms:
dxy2 + dx3 + -1dy2 = 0

Solving
dxy2 + dx3 + -1dy2 = 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(xy2 + x3 + -1y2) = 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 '(xy2 + x3 + -1y2)' equal to zero and attempt to solve:

Simplifying
xy2 + x3 + -1y2 = 0

Solving
xy2 + x3 + -1y2 = 0

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

Add '-1xy2' to each side of the equation.
xy2 + x3 + -1xy2 + -1y2 = 0 + -1xy2

Reorder the terms:
xy2 + -1xy2 + x3 + -1y2 = 0 + -1xy2

Combine like terms: xy2 + -1xy2 = 0
0 + x3 + -1y2 = 0 + -1xy2
x3 + -1y2 = 0 + -1xy2
Remove the zero:
x3 + -1y2 = -1xy2

Add '-1x3' to each side of the equation.
x3 + -1x3 + -1y2 = -1xy2 + -1x3

Combine like terms: x3 + -1x3 = 0
0 + -1y2 = -1xy2 + -1x3
-1y2 = -1xy2 + -1x3

Add 'y2' to each side of the equation.
-1y2 + y2 = -1xy2 + -1x3 + y2

Combine like terms: -1y2 + y2 = 0
0 = -1xy2 + -1x3 + y2

Simplifying
0 = -1xy2 + -1x3 + y2

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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