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

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


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

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

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

Reorder the terms:
(dx2y + 1dy) = (3 + -4xy) * dx
(dx2y + 1dy) = (3 + -4xy) * dx

Reorder the terms for easier multiplication:
dx2y + 1dy = dx(3 + -4xy)
dx2y + 1dy = (3 * dx + -4xy * dx)
dx2y + 1dy = (3dx + -4dx2y)

Solving
dx2y + 1dy = 3dx + -4dx2y

Solving for variable 'd'.

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

Add '-3dx' to each side of the equation.
dx2y + -3dx + 1dy = 3dx + -3dx + -4dx2y

Reorder the terms:
-3dx + dx2y + 1dy = 3dx + -3dx + -4dx2y

Combine like terms: 3dx + -3dx = 0
-3dx + dx2y + 1dy = 0 + -4dx2y
-3dx + dx2y + 1dy = -4dx2y

Add '4dx2y' to each side of the equation.
-3dx + dx2y + 4dx2y + 1dy = -4dx2y + 4dx2y

Combine like terms: dx2y + 4dx2y = 5dx2y
-3dx + 5dx2y + 1dy = -4dx2y + 4dx2y

Combine like terms: -4dx2y + 4dx2y = 0
-3dx + 5dx2y + 1dy = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(-3x + 5x2y + y) = 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 '(-3x + 5x2y + y)' equal to zero and attempt to solve:

Simplifying
-3x + 5x2y + y = 0

Solving
-3x + 5x2y + y = 0

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

Add '3x' to each side of the equation.
-3x + 5x2y + 3x + y = 0 + 3x

Reorder the terms:
-3x + 3x + 5x2y + y = 0 + 3x

Combine like terms: -3x + 3x = 0
0 + 5x2y + y = 0 + 3x
5x2y + y = 0 + 3x
Remove the zero:
5x2y + y = 3x

Add '-5x2y' to each side of the equation.
5x2y + -5x2y + y = 3x + -5x2y

Combine like terms: 5x2y + -5x2y = 0
0 + y = 3x + -5x2y
y = 3x + -5x2y

Add '-1y' to each side of the equation.
y + -1y = 3x + -5x2y + -1y

Combine like terms: y + -1y = 0
0 = 3x + -5x2y + -1y

Simplifying
0 = 3x + -5x2y + -1y

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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