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

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


Simplifying
(y + -3x2) * dx + (x + -1) * dy = 0

Reorder the terms:
(-3x2 + y) * dx + (x + -1) * dy = 0

Reorder the terms for easier multiplication:
dx(-3x2 + y) + (x + -1) * dy = 0
(-3x2 * dx + y * dx) + (x + -1) * dy = 0

Reorder the terms:
(dxy + -3dx3) + (x + -1) * dy = 0
(dxy + -3dx3) + (x + -1) * dy = 0

Reorder the terms:
dxy + -3dx3 + (-1 + x) * dy = 0

Reorder the terms for easier multiplication:
dxy + -3dx3 + dy(-1 + x) = 0
dxy + -3dx3 + (-1 * dy + x * dy) = 0

Reorder the terms:
dxy + -3dx3 + (dxy + -1dy) = 0
dxy + -3dx3 + (dxy + -1dy) = 0

Reorder the terms:
dxy + dxy + -3dx3 + -1dy = 0

Combine like terms: dxy + dxy = 2dxy
2dxy + -3dx3 + -1dy = 0

Solving
2dxy + -3dx3 + -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 + -3x3 + -1y) = 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 + -3x3 + -1y)' equal to zero and attempt to solve:

Simplifying
2xy + -3x3 + -1y = 0

Solving
2xy + -3x3 + -1y = 0

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

Add '-2xy' to each side of the equation.
2xy + -3x3 + -2xy + -1y = 0 + -2xy

Reorder the terms:
2xy + -2xy + -3x3 + -1y = 0 + -2xy

Combine like terms: 2xy + -2xy = 0
0 + -3x3 + -1y = 0 + -2xy
-3x3 + -1y = 0 + -2xy
Remove the zero:
-3x3 + -1y = -2xy

Add '3x3' to each side of the equation.
-3x3 + 3x3 + -1y = -2xy + 3x3

Combine like terms: -3x3 + 3x3 = 0
0 + -1y = -2xy + 3x3
-1y = -2xy + 3x3

Add 'y' to each side of the equation.
-1y + y = -2xy + 3x3 + y

Combine like terms: -1y + y = 0
0 = -2xy + 3x3 + y

Simplifying
0 = -2xy + 3x3 + y

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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