(x^2+1)dx=(3-4xy)dy

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


Simplifying
(x2 + 1) * dx = (3 + -4xy) * dy

Reorder the terms:
(1 + x2) * dx = (3 + -4xy) * dy

Reorder the terms for easier multiplication:
dx(1 + x2) = (3 + -4xy) * dy
(1 * dx + x2 * dx) = (3 + -4xy) * dy
(1dx + dx3) = (3 + -4xy) * dy

Reorder the terms for easier multiplication:
1dx + dx3 = dy(3 + -4xy)
1dx + dx3 = (3 * dy + -4xy * dy)

Reorder the terms:
1dx + dx3 = (-4dxy2 + 3dy)
1dx + dx3 = (-4dxy2 + 3dy)

Solving
1dx + dx3 = -4dxy2 + 3dy

Solving for variable 'd'.

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

Add '4dxy2' to each side of the equation.
1dx + 4dxy2 + dx3 = -4dxy2 + 4dxy2 + 3dy

Combine like terms: -4dxy2 + 4dxy2 = 0
1dx + 4dxy2 + dx3 = 0 + 3dy
1dx + 4dxy2 + dx3 = 3dy

Add '-3dy' to each side of the equation.
1dx + 4dxy2 + dx3 + -3dy = 3dy + -3dy

Combine like terms: 3dy + -3dy = 0
1dx + 4dxy2 + dx3 + -3dy = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(x + 4xy2 + x3 + -3y) = 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 '(x + 4xy2 + x3 + -3y)' equal to zero and attempt to solve:

Simplifying
x + 4xy2 + x3 + -3y = 0

Solving
x + 4xy2 + x3 + -3y = 0

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

Add '-1x' to each side of the equation.
x + 4xy2 + x3 + -1x + -3y = 0 + -1x

Reorder the terms:
x + -1x + 4xy2 + x3 + -3y = 0 + -1x

Combine like terms: x + -1x = 0
0 + 4xy2 + x3 + -3y = 0 + -1x
4xy2 + x3 + -3y = 0 + -1x
Remove the zero:
4xy2 + x3 + -3y = -1x

Add '-4xy2' to each side of the equation.
4xy2 + x3 + -4xy2 + -3y = -1x + -4xy2

Reorder the terms:
4xy2 + -4xy2 + x3 + -3y = -1x + -4xy2

Combine like terms: 4xy2 + -4xy2 = 0
0 + x3 + -3y = -1x + -4xy2
x3 + -3y = -1x + -4xy2

Add '-1x3' to each side of the equation.
x3 + -1x3 + -3y = -1x + -4xy2 + -1x3

Combine like terms: x3 + -1x3 = 0
0 + -3y = -1x + -4xy2 + -1x3
-3y = -1x + -4xy2 + -1x3

Add '3y' to each side of the equation.
-3y + 3y = -1x + -4xy2 + -1x3 + 3y

Combine like terms: -3y + 3y = 0
0 = -1x + -4xy2 + -1x3 + 3y

Simplifying
0 = -1x + -4xy2 + -1x3 + 3y

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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