(5x+7y)dx+(7x-8y^3)dy=0

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Solution for (5x+7y)dx+(7x-8y^3)dy=0 equation: 


Simplifying
(5x + 7y) * dx + (7x + -8y3) * dy = 0

Reorder the terms for easier multiplication:
dx(5x + 7y) + (7x + -8y3) * dy = 0
(5x * dx + 7y * dx) + (7x + -8y3) * dy = 0

Reorder the terms:
(7dxy + 5dx2) + (7x + -8y3) * dy = 0
(7dxy + 5dx2) + (7x + -8y3) * dy = 0

Reorder the terms for easier multiplication:
7dxy + 5dx2 + dy(7x + -8y3) = 0
7dxy + 5dx2 + (7x * dy + -8y3 * dy) = 0
7dxy + 5dx2 + (7dxy + -8dy4) = 0

Reorder the terms:
7dxy + 7dxy + 5dx2 + -8dy4 = 0

Combine like terms: 7dxy + 7dxy = 14dxy
14dxy + 5dx2 + -8dy4 = 0

Solving
14dxy + 5dx2 + -8dy4 = 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(14xy + 5x2 + -8y4) = 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 '(14xy + 5x2 + -8y4)' equal to zero and attempt to solve:

Simplifying
14xy + 5x2 + -8y4 = 0

Solving
14xy + 5x2 + -8y4 = 0

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

Add '-14xy' to each side of the equation.
14xy + 5x2 + -14xy + -8y4 = 0 + -14xy

Reorder the terms:
14xy + -14xy + 5x2 + -8y4 = 0 + -14xy

Combine like terms: 14xy + -14xy = 0
0 + 5x2 + -8y4 = 0 + -14xy
5x2 + -8y4 = 0 + -14xy
Remove the zero:
5x2 + -8y4 = -14xy

Add '-5x2' to each side of the equation.
5x2 + -5x2 + -8y4 = -14xy + -5x2

Combine like terms: 5x2 + -5x2 = 0
0 + -8y4 = -14xy + -5x2
-8y4 = -14xy + -5x2

Add '8y4' to each side of the equation.
-8y4 + 8y4 = -14xy + -5x2 + 8y4

Combine like terms: -8y4 + 8y4 = 0
0 = -14xy + -5x2 + 8y4

Simplifying
0 = -14xy + -5x2 + 8y4

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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