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

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


Simplifying
(7x2 + 2xy + y7) * dx + (x2 + y6) * dy = 0

Reorder the terms:
(2xy + 7x2 + y7) * dx + (x2 + y6) * dy = 0

Reorder the terms for easier multiplication:
dx(2xy + 7x2 + y7) + (x2 + y6) * dy = 0
(2xy * dx + 7x2 * dx + y7 * dx) + (x2 + y6) * dy = 0

Reorder the terms:
(dxy7 + 2dx2y + 7dx3) + (x2 + y6) * dy = 0
(dxy7 + 2dx2y + 7dx3) + (x2 + y6) * dy = 0

Reorder the terms for easier multiplication:
dxy7 + 2dx2y + 7dx3 + dy(x2 + y6) = 0
dxy7 + 2dx2y + 7dx3 + (x2 * dy + y6 * dy) = 0
dxy7 + 2dx2y + 7dx3 + (dx2y + dy7) = 0

Reorder the terms:
dxy7 + 2dx2y + dx2y + 7dx3 + dy7 = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
dxy7 + 3dx2y + 7dx3 + dy7 = 0

Solving
dxy7 + 3dx2y + 7dx3 + dy7 = 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(xy7 + 3x2y + 7x3 + y7) = 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 '(xy7 + 3x2y + 7x3 + y7)' equal to zero and attempt to solve:

Simplifying
xy7 + 3x2y + 7x3 + y7 = 0

Solving
xy7 + 3x2y + 7x3 + y7 = 0

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

Add '-1xy7' to each side of the equation.
xy7 + 3x2y + 7x3 + -1xy7 + y7 = 0 + -1xy7

Reorder the terms:
xy7 + -1xy7 + 3x2y + 7x3 + y7 = 0 + -1xy7

Combine like terms: xy7 + -1xy7 = 0
0 + 3x2y + 7x3 + y7 = 0 + -1xy7
3x2y + 7x3 + y7 = 0 + -1xy7
Remove the zero:
3x2y + 7x3 + y7 = -1xy7

Add '-3x2y' to each side of the equation.
3x2y + 7x3 + -3x2y + y7 = -1xy7 + -3x2y

Reorder the terms:
3x2y + -3x2y + 7x3 + y7 = -1xy7 + -3x2y

Combine like terms: 3x2y + -3x2y = 0
0 + 7x3 + y7 = -1xy7 + -3x2y
7x3 + y7 = -1xy7 + -3x2y

Add '-7x3' to each side of the equation.
7x3 + -7x3 + y7 = -1xy7 + -3x2y + -7x3

Combine like terms: 7x3 + -7x3 = 0
0 + y7 = -1xy7 + -3x2y + -7x3
y7 = -1xy7 + -3x2y + -7x3

Add '-1y7' to each side of the equation.
y7 + -1y7 = -1xy7 + -3x2y + -7x3 + -1y7

Combine like terms: y7 + -1y7 = 0
0 = -1xy7 + -3x2y + -7x3 + -1y7

Simplifying
0 = -1xy7 + -3x2y + -7x3 + -1y7

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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