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

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


Simplifying
(2x2y + 2y + 5) * dx + (2x3 + -2x) * dy = 0

Reorder the terms:
(5 + 2x2y + 2y) * dx + (2x3 + -2x) * dy = 0

Reorder the terms for easier multiplication:
dx(5 + 2x2y + 2y) + (2x3 + -2x) * dy = 0
(5 * dx + 2x2y * dx + 2y * dx) + (2x3 + -2x) * dy = 0

Reorder the terms:
(5dx + 2dxy + 2dx3y) + (2x3 + -2x) * dy = 0
(5dx + 2dxy + 2dx3y) + (2x3 + -2x) * dy = 0

Reorder the terms:
5dx + 2dxy + 2dx3y + (-2x + 2x3) * dy = 0

Reorder the terms for easier multiplication:
5dx + 2dxy + 2dx3y + dy(-2x + 2x3) = 0
5dx + 2dxy + 2dx3y + (-2x * dy + 2x3 * dy) = 0
5dx + 2dxy + 2dx3y + (-2dxy + 2dx3y) = 0

Reorder the terms:
5dx + 2dxy + -2dxy + 2dx3y + 2dx3y = 0

Combine like terms: 2dxy + -2dxy = 0
5dx + 0 + 2dx3y + 2dx3y = 0
5dx + 2dx3y + 2dx3y = 0

Combine like terms: 2dx3y + 2dx3y = 4dx3y
5dx + 4dx3y = 0

Solving
5dx + 4dx3y = 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), 'dx'.
dx(5 + 4x2y) = 0


Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve:

Simplifying
dx = 0

Solving
dx = 0

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

Simplifying
dx = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(5 + 4x2y)' equal to zero and attempt to solve:

Simplifying
5 + 4x2y = 0

Solving
5 + 4x2y = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4x2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x2y = 0 + -5
4x2y = 0 + -5

Combine like terms: 0 + -5 = -5
4x2y = -5

Add '-4x2y' to each side of the equation.
4x2y + -4x2y = -5 + -4x2y

Combine like terms: 4x2y + -4x2y = 0
0 = -5 + -4x2y

Simplifying
0 = -5 + -4x2y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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