(5x^4+3x^2y^2-2xy^3)dx+(2x^3y-3x^2y^2-5y)dy=0

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Solution for (5x^4+3x^2y^2-2xy^3)dx+(2x^3y-3x^2y^2-5y)dy=0 equation: 


Simplifying
(5x4 + 3x2y2 + -2xy3) * dx + (2x3y + -3x2y2 + -5y) * dy = 0

Reorder the terms:
(-2xy3 + 3x2y2 + 5x4) * dx + (2x3y + -3x2y2 + -5y) * dy = 0

Reorder the terms for easier multiplication:
dx(-2xy3 + 3x2y2 + 5x4) + (2x3y + -3x2y2 + -5y) * dy = 0
(-2xy3 * dx + 3x2y2 * dx + 5x4 * dx) + (2x3y + -3x2y2 + -5y) * dy = 0
(-2dx2y3 + 3dx3y2 + 5dx5) + (2x3y + -3x2y2 + -5y) * dy = 0

Reorder the terms:
-2dx2y3 + 3dx3y2 + 5dx5 + (-3x2y2 + 2x3y + -5y) * dy = 0

Reorder the terms for easier multiplication:
-2dx2y3 + 3dx3y2 + 5dx5 + dy(-3x2y2 + 2x3y + -5y) = 0
-2dx2y3 + 3dx3y2 + 5dx5 + (-3x2y2 * dy + 2x3y * dy + -5y * dy) = 0
-2dx2y3 + 3dx3y2 + 5dx5 + (-3dx2y3 + 2dx3y2 + -5dy2) = 0

Reorder the terms:
-2dx2y3 + -3dx2y3 + 3dx3y2 + 2dx3y2 + 5dx5 + -5dy2 = 0

Combine like terms: -2dx2y3 + -3dx2y3 = -5dx2y3
-5dx2y3 + 3dx3y2 + 2dx3y2 + 5dx5 + -5dy2 = 0

Combine like terms: 3dx3y2 + 2dx3y2 = 5dx3y2
-5dx2y3 + 5dx3y2 + 5dx5 + -5dy2 = 0

Solving
-5dx2y3 + 5dx3y2 + 5dx5 + -5dy2 = 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), '5d'.
5d(-1x2y3 + x3y2 + x5 + -1y2) = 0

Ignore the factor 5.

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 '(-1x2y3 + x3y2 + x5 + -1y2)' equal to zero and attempt to solve:

Simplifying
-1x2y3 + x3y2 + x5 + -1y2 = 0

Solving
-1x2y3 + x3y2 + x5 + -1y2 = 0

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

Add 'x2y3' to each side of the equation.
-1x2y3 + x3y2 + x5 + x2y3 + -1y2 = 0 + x2y3

Reorder the terms:
-1x2y3 + x2y3 + x3y2 + x5 + -1y2 = 0 + x2y3

Combine like terms: -1x2y3 + x2y3 = 0
0 + x3y2 + x5 + -1y2 = 0 + x2y3
x3y2 + x5 + -1y2 = 0 + x2y3
Remove the zero:
x3y2 + x5 + -1y2 = x2y3

Add '-1x3y2' to each side of the equation.
x3y2 + x5 + -1x3y2 + -1y2 = x2y3 + -1x3y2

Reorder the terms:
x3y2 + -1x3y2 + x5 + -1y2 = x2y3 + -1x3y2

Combine like terms: x3y2 + -1x3y2 = 0
0 + x5 + -1y2 = x2y3 + -1x3y2
x5 + -1y2 = x2y3 + -1x3y2

Add '-1x5' to each side of the equation.
x5 + -1x5 + -1y2 = x2y3 + -1x3y2 + -1x5

Combine like terms: x5 + -1x5 = 0
0 + -1y2 = x2y3 + -1x3y2 + -1x5
-1y2 = x2y3 + -1x3y2 + -1x5

Add 'y2' to each side of the equation.
-1y2 + y2 = x2y3 + -1x3y2 + -1x5 + y2

Combine like terms: -1y2 + y2 = 0
0 = x2y3 + -1x3y2 + -1x5 + y2

Simplifying
0 = x2y3 + -1x3y2 + -1x5 + 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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