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

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


Simplifying
(5xy2 + -1x3) * dx + (5x2y + -1y) * dy = 0

Reorder the terms for easier multiplication:
dx(5xy2 + -1x3) + (5x2y + -1y) * dy = 0
(5xy2 * dx + -1x3 * dx) + (5x2y + -1y) * dy = 0
(5dx2y2 + -1dx4) + (5x2y + -1y) * dy = 0

Reorder the terms for easier multiplication:
5dx2y2 + -1dx4 + dy(5x2y + -1y) = 0
5dx2y2 + -1dx4 + (5x2y * dy + -1y * dy) = 0
5dx2y2 + -1dx4 + (5dx2y2 + -1dy2) = 0

Reorder the terms:
5dx2y2 + 5dx2y2 + -1dx4 + -1dy2 = 0

Combine like terms: 5dx2y2 + 5dx2y2 = 10dx2y2
10dx2y2 + -1dx4 + -1dy2 = 0

Solving
10dx2y2 + -1dx4 + -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(10x2y2 + -1x4 + -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 '(10x2y2 + -1x4 + -1y2)' equal to zero and attempt to solve:

Simplifying
10x2y2 + -1x4 + -1y2 = 0

Solving
10x2y2 + -1x4 + -1y2 = 0

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

Add '-10x2y2' to each side of the equation.
10x2y2 + -1x4 + -10x2y2 + -1y2 = 0 + -10x2y2

Reorder the terms:
10x2y2 + -10x2y2 + -1x4 + -1y2 = 0 + -10x2y2

Combine like terms: 10x2y2 + -10x2y2 = 0
0 + -1x4 + -1y2 = 0 + -10x2y2
-1x4 + -1y2 = 0 + -10x2y2
Remove the zero:
-1x4 + -1y2 = -10x2y2

Add 'x4' to each side of the equation.
-1x4 + x4 + -1y2 = -10x2y2 + x4

Combine like terms: -1x4 + x4 = 0
0 + -1y2 = -10x2y2 + x4
-1y2 = -10x2y2 + x4

Add 'y2' to each side of the equation.
-1y2 + y2 = -10x2y2 + x4 + y2

Combine like terms: -1y2 + y2 = 0
0 = -10x2y2 + x4 + y2

Simplifying
0 = -10x2y2 + x4 + 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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