(4x^3y-15x^2-y)dx+(x^4+3y^2-x)dy=0

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Solution for (4x^3y-15x^2-y)dx+(x^4+3y^2-x)dy=0 equation: 


Simplifying
(4x3y + -15x2 + -1y) * dx + (x4 + 3y2 + -1x) * dy = 0

Reorder the terms:
(-15x2 + 4x3y + -1y) * dx + (x4 + 3y2 + -1x) * dy = 0

Reorder the terms for easier multiplication:
dx(-15x2 + 4x3y + -1y) + (x4 + 3y2 + -1x) * dy = 0
(-15x2 * dx + 4x3y * dx + -1y * dx) + (x4 + 3y2 + -1x) * dy = 0

Reorder the terms:
(-1dxy + -15dx3 + 4dx4y) + (x4 + 3y2 + -1x) * dy = 0
(-1dxy + -15dx3 + 4dx4y) + (x4 + 3y2 + -1x) * dy = 0

Reorder the terms:
-1dxy + -15dx3 + 4dx4y + (-1x + x4 + 3y2) * dy = 0

Reorder the terms for easier multiplication:
-1dxy + -15dx3 + 4dx4y + dy(-1x + x4 + 3y2) = 0
-1dxy + -15dx3 + 4dx4y + (-1x * dy + x4 * dy + 3y2 * dy) = 0
-1dxy + -15dx3 + 4dx4y + (-1dxy + dx4y + 3dy3) = 0

Reorder the terms:
-1dxy + -1dxy + -15dx3 + 4dx4y + dx4y + 3dy3 = 0

Combine like terms: -1dxy + -1dxy = -2dxy
-2dxy + -15dx3 + 4dx4y + dx4y + 3dy3 = 0

Combine like terms: 4dx4y + dx4y = 5dx4y
-2dxy + -15dx3 + 5dx4y + 3dy3 = 0

Solving
-2dxy + -15dx3 + 5dx4y + 3dy3 = 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 + -15x3 + 5x4y + 3y3) = 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 + -15x3 + 5x4y + 3y3)' equal to zero and attempt to solve:

Simplifying
-2xy + -15x3 + 5x4y + 3y3 = 0

Solving
-2xy + -15x3 + 5x4y + 3y3 = 0

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

Add '2xy' to each side of the equation.
-2xy + -15x3 + 5x4y + 2xy + 3y3 = 0 + 2xy

Reorder the terms:
-2xy + 2xy + -15x3 + 5x4y + 3y3 = 0 + 2xy

Combine like terms: -2xy + 2xy = 0
0 + -15x3 + 5x4y + 3y3 = 0 + 2xy
-15x3 + 5x4y + 3y3 = 0 + 2xy
Remove the zero:
-15x3 + 5x4y + 3y3 = 2xy

Add '15x3' to each side of the equation.
-15x3 + 5x4y + 15x3 + 3y3 = 2xy + 15x3

Reorder the terms:
-15x3 + 15x3 + 5x4y + 3y3 = 2xy + 15x3

Combine like terms: -15x3 + 15x3 = 0
0 + 5x4y + 3y3 = 2xy + 15x3
5x4y + 3y3 = 2xy + 15x3

Add '-5x4y' to each side of the equation.
5x4y + -5x4y + 3y3 = 2xy + 15x3 + -5x4y

Combine like terms: 5x4y + -5x4y = 0
0 + 3y3 = 2xy + 15x3 + -5x4y
3y3 = 2xy + 15x3 + -5x4y

Add '-3y3' to each side of the equation.
3y3 + -3y3 = 2xy + 15x3 + -5x4y + -3y3

Combine like terms: 3y3 + -3y3 = 0
0 = 2xy + 15x3 + -5x4y + -3y3

Simplifying
0 = 2xy + 15x3 + -5x4y + -3y3

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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