(7x^4+xy^2)dx+(x^2y+6y^5)dy=0

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Solution for (7x^4+xy^2)dx+(x^2y+6y^5)dy=0 equation: 


Simplifying
(7x4 + xy2) * dx + (x2y + 6y5) * dy = 0

Reorder the terms:
(xy2 + 7x4) * dx + (x2y + 6y5) * dy = 0

Reorder the terms for easier multiplication:
dx(xy2 + 7x4) + (x2y + 6y5) * dy = 0
(xy2 * dx + 7x4 * dx) + (x2y + 6y5) * dy = 0
(dx2y2 + 7dx5) + (x2y + 6y5) * dy = 0

Reorder the terms for easier multiplication:
dx2y2 + 7dx5 + dy(x2y + 6y5) = 0
dx2y2 + 7dx5 + (x2y * dy + 6y5 * dy) = 0
dx2y2 + 7dx5 + (dx2y2 + 6dy6) = 0

Reorder the terms:
dx2y2 + dx2y2 + 7dx5 + 6dy6 = 0

Combine like terms: dx2y2 + dx2y2 = 2dx2y2
2dx2y2 + 7dx5 + 6dy6 = 0

Solving
2dx2y2 + 7dx5 + 6dy6 = 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(2x2y2 + 7x5 + 6y6) = 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 '(2x2y2 + 7x5 + 6y6)' equal to zero and attempt to solve:

Simplifying
2x2y2 + 7x5 + 6y6 = 0

Solving
2x2y2 + 7x5 + 6y6 = 0

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

Add '-2x2y2' to each side of the equation.
2x2y2 + 7x5 + -2x2y2 + 6y6 = 0 + -2x2y2

Reorder the terms:
2x2y2 + -2x2y2 + 7x5 + 6y6 = 0 + -2x2y2

Combine like terms: 2x2y2 + -2x2y2 = 0
0 + 7x5 + 6y6 = 0 + -2x2y2
7x5 + 6y6 = 0 + -2x2y2
Remove the zero:
7x5 + 6y6 = -2x2y2

Add '-7x5' to each side of the equation.
7x5 + -7x5 + 6y6 = -2x2y2 + -7x5

Combine like terms: 7x5 + -7x5 = 0
0 + 6y6 = -2x2y2 + -7x5
6y6 = -2x2y2 + -7x5

Add '-6y6' to each side of the equation.
6y6 + -6y6 = -2x2y2 + -7x5 + -6y6

Combine like terms: 6y6 + -6y6 = 0
0 = -2x2y2 + -7x5 + -6y6

Simplifying
0 = -2x2y2 + -7x5 + -6y6

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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