(7x^3+3x^2y+4y)dx+(4x^3+x+5y)dy=0

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Solution for (7x^3+3x^2y+4y)dx+(4x^3+x+5y)dy=0 equation: 


Simplifying
(7x3 + 3x2y + 4y) * dx + (4x3 + x + 5y) * dy = 0

Reorder the terms:
(3x2y + 7x3 + 4y) * dx + (4x3 + x + 5y) * dy = 0

Reorder the terms for easier multiplication:
dx(3x2y + 7x3 + 4y) + (4x3 + x + 5y) * dy = 0
(3x2y * dx + 7x3 * dx + 4y * dx) + (4x3 + x + 5y) * dy = 0

Reorder the terms:
(4dxy + 3dx3y + 7dx4) + (4x3 + x + 5y) * dy = 0
(4dxy + 3dx3y + 7dx4) + (4x3 + x + 5y) * dy = 0

Reorder the terms:
4dxy + 3dx3y + 7dx4 + (x + 4x3 + 5y) * dy = 0

Reorder the terms for easier multiplication:
4dxy + 3dx3y + 7dx4 + dy(x + 4x3 + 5y) = 0
4dxy + 3dx3y + 7dx4 + (x * dy + 4x3 * dy + 5y * dy) = 0
4dxy + 3dx3y + 7dx4 + (dxy + 4dx3y + 5dy2) = 0

Reorder the terms:
4dxy + dxy + 3dx3y + 4dx3y + 7dx4 + 5dy2 = 0

Combine like terms: 4dxy + dxy = 5dxy
5dxy + 3dx3y + 4dx3y + 7dx4 + 5dy2 = 0

Combine like terms: 3dx3y + 4dx3y = 7dx3y
5dxy + 7dx3y + 7dx4 + 5dy2 = 0

Solving
5dxy + 7dx3y + 7dx4 + 5dy2 = 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(5xy + 7x3y + 7x4 + 5y2) = 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 '(5xy + 7x3y + 7x4 + 5y2)' equal to zero and attempt to solve:

Simplifying
5xy + 7x3y + 7x4 + 5y2 = 0

Solving
5xy + 7x3y + 7x4 + 5y2 = 0

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

Add '-5xy' to each side of the equation.
5xy + 7x3y + 7x4 + -5xy + 5y2 = 0 + -5xy

Reorder the terms:
5xy + -5xy + 7x3y + 7x4 + 5y2 = 0 + -5xy

Combine like terms: 5xy + -5xy = 0
0 + 7x3y + 7x4 + 5y2 = 0 + -5xy
7x3y + 7x4 + 5y2 = 0 + -5xy
Remove the zero:
7x3y + 7x4 + 5y2 = -5xy

Add '-7x3y' to each side of the equation.
7x3y + 7x4 + -7x3y + 5y2 = -5xy + -7x3y

Reorder the terms:
7x3y + -7x3y + 7x4 + 5y2 = -5xy + -7x3y

Combine like terms: 7x3y + -7x3y = 0
0 + 7x4 + 5y2 = -5xy + -7x3y
7x4 + 5y2 = -5xy + -7x3y

Add '-7x4' to each side of the equation.
7x4 + -7x4 + 5y2 = -5xy + -7x3y + -7x4

Combine like terms: 7x4 + -7x4 = 0
0 + 5y2 = -5xy + -7x3y + -7x4
5y2 = -5xy + -7x3y + -7x4

Add '-5y2' to each side of the equation.
5y2 + -5y2 = -5xy + -7x3y + -7x4 + -5y2

Combine like terms: 5y2 + -5y2 = 0
0 = -5xy + -7x3y + -7x4 + -5y2

Simplifying
0 = -5xy + -7x3y + -7x4 + -5y2

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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