(x^2+4y+7)dx+(2x-y^3+1)dy=0

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Solution for (x^2+4y+7)dx+(2x-y^3+1)dy=0 equation: 


Simplifying
(x2 + 4y + 7) * dx + (2x + -1y3 + 1) * dy = 0

Reorder the terms:
(7 + x2 + 4y) * dx + (2x + -1y3 + 1) * dy = 0

Reorder the terms for easier multiplication:
dx(7 + x2 + 4y) + (2x + -1y3 + 1) * dy = 0
(7 * dx + x2 * dx + 4y * dx) + (2x + -1y3 + 1) * dy = 0

Reorder the terms:
(7dx + 4dxy + dx3) + (2x + -1y3 + 1) * dy = 0
(7dx + 4dxy + dx3) + (2x + -1y3 + 1) * dy = 0

Reorder the terms:
7dx + 4dxy + dx3 + (1 + 2x + -1y3) * dy = 0

Reorder the terms for easier multiplication:
7dx + 4dxy + dx3 + dy(1 + 2x + -1y3) = 0
7dx + 4dxy + dx3 + (1 * dy + 2x * dy + -1y3 * dy) = 0

Reorder the terms:
7dx + 4dxy + dx3 + (2dxy + 1dy + -1dy4) = 0
7dx + 4dxy + dx3 + (2dxy + 1dy + -1dy4) = 0

Reorder the terms:
7dx + 4dxy + 2dxy + dx3 + 1dy + -1dy4 = 0

Combine like terms: 4dxy + 2dxy = 6dxy
7dx + 6dxy + dx3 + 1dy + -1dy4 = 0

Solving
7dx + 6dxy + dx3 + 1dy + -1dy4 = 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(7x + 6xy + x3 + y + -1y4) = 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 '(7x + 6xy + x3 + y + -1y4)' equal to zero and attempt to solve:

Simplifying
7x + 6xy + x3 + y + -1y4 = 0

Solving
7x + 6xy + x3 + y + -1y4 = 0

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

Add '-7x' to each side of the equation.
7x + 6xy + x3 + y + -7x + -1y4 = 0 + -7x

Reorder the terms:
7x + -7x + 6xy + x3 + y + -1y4 = 0 + -7x

Combine like terms: 7x + -7x = 0
0 + 6xy + x3 + y + -1y4 = 0 + -7x
6xy + x3 + y + -1y4 = 0 + -7x
Remove the zero:
6xy + x3 + y + -1y4 = -7x

Add '-6xy' to each side of the equation.
6xy + x3 + y + -6xy + -1y4 = -7x + -6xy

Reorder the terms:
6xy + -6xy + x3 + y + -1y4 = -7x + -6xy

Combine like terms: 6xy + -6xy = 0
0 + x3 + y + -1y4 = -7x + -6xy
x3 + y + -1y4 = -7x + -6xy

Add '-1x3' to each side of the equation.
x3 + y + -1x3 + -1y4 = -7x + -6xy + -1x3

Reorder the terms:
x3 + -1x3 + y + -1y4 = -7x + -6xy + -1x3

Combine like terms: x3 + -1x3 = 0
0 + y + -1y4 = -7x + -6xy + -1x3
y + -1y4 = -7x + -6xy + -1x3

Add '-1y' to each side of the equation.
y + -1y + -1y4 = -7x + -6xy + -1x3 + -1y

Combine like terms: y + -1y = 0
0 + -1y4 = -7x + -6xy + -1x3 + -1y
-1y4 = -7x + -6xy + -1x3 + -1y

Add 'y4' to each side of the equation.
-1y4 + y4 = -7x + -6xy + -1x3 + -1y + y4

Combine like terms: -1y4 + y4 = 0
0 = -7x + -6xy + -1x3 + -1y + y4

Simplifying
0 = -7x + -6xy + -1x3 + -1y + y4

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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