(y-3x^2)dx-(4y-x)dy=0

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Solution for (y-3x^2)dx-(4y-x)dy=0 equation: 


Simplifying
(y + -3x2) * dx + -1(4y + -1x) * dy = 0

Reorder the terms:
(-3x2 + y) * dx + -1(4y + -1x) * dy = 0

Reorder the terms for easier multiplication:
dx(-3x2 + y) + -1(4y + -1x) * dy = 0
(-3x2 * dx + y * dx) + -1(4y + -1x) * dy = 0

Reorder the terms:
(dxy + -3dx3) + -1(4y + -1x) * dy = 0
(dxy + -3dx3) + -1(4y + -1x) * dy = 0

Reorder the terms:
dxy + -3dx3 + -1(-1x + 4y) * dy = 0

Reorder the terms for easier multiplication:
dxy + -3dx3 + -1dy(-1x + 4y) = 0
dxy + -3dx3 + (-1x * -1dy + 4y * -1dy) = 0
dxy + -3dx3 + (1dxy + -4dy2) = 0

Reorder the terms:
dxy + 1dxy + -3dx3 + -4dy2 = 0

Combine like terms: dxy + 1dxy = 2dxy
2dxy + -3dx3 + -4dy2 = 0

Solving
2dxy + -3dx3 + -4dy2 = 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 + -4y2) = 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 + -4y2)' equal to zero and attempt to solve:

Simplifying
2xy + -3x3 + -4y2 = 0

Solving
2xy + -3x3 + -4y2 = 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 + -4y2 = 0 + -2xy

Reorder the terms:
2xy + -2xy + -3x3 + -4y2 = 0 + -2xy

Combine like terms: 2xy + -2xy = 0
0 + -3x3 + -4y2 = 0 + -2xy
-3x3 + -4y2 = 0 + -2xy
Remove the zero:
-3x3 + -4y2 = -2xy

Add '3x3' to each side of the equation.
-3x3 + 3x3 + -4y2 = -2xy + 3x3

Combine like terms: -3x3 + 3x3 = 0
0 + -4y2 = -2xy + 3x3
-4y2 = -2xy + 3x3

Add '4y2' to each side of the equation.
-4y2 + 4y2 = -2xy + 3x3 + 4y2

Combine like terms: -4y2 + 4y2 = 0
0 = -2xy + 3x3 + 4y2

Simplifying
0 = -2xy + 3x3 + 4y2

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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