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

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


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

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

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

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

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

Combine like terms: 5dxy + 5dxy = 10dxy
10dxy + 7dx2 + -8dy4 = 0

Solving
10dxy + 7dx2 + -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(10xy + 7x2 + -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 '(10xy + 7x2 + -8y4)' equal to zero and attempt to solve:

Simplifying
10xy + 7x2 + -8y4 = 0

Solving
10xy + 7x2 + -8y4 = 0

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

Add '-10xy' to each side of the equation.
10xy + 7x2 + -10xy + -8y4 = 0 + -10xy

Reorder the terms:
10xy + -10xy + 7x2 + -8y4 = 0 + -10xy

Combine like terms: 10xy + -10xy = 0
0 + 7x2 + -8y4 = 0 + -10xy
7x2 + -8y4 = 0 + -10xy
Remove the zero:
7x2 + -8y4 = -10xy

Add '-7x2' to each side of the equation.
7x2 + -7x2 + -8y4 = -10xy + -7x2

Combine like terms: 7x2 + -7x2 = 0
0 + -8y4 = -10xy + -7x2
-8y4 = -10xy + -7x2

Add '8y4' to each side of the equation.
-8y4 + 8y4 = -10xy + -7x2 + 8y4

Combine like terms: -8y4 + 8y4 = 0
0 = -10xy + -7x2 + 8y4

Simplifying
0 = -10xy + -7x2 + 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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