(x+4y^2x)dy+2ydx=0

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Solution for (x+4y^2x)dy+2ydx=0 equation: 


Simplifying
(x + 4y2x) * dy + 2ydx = 0

Reorder the terms for easier multiplication:
dy(x + 4xy2) + 2ydx = 0
(x * dy + 4xy2 * dy) + 2ydx = 0
(dxy + 4dxy3) + 2ydx = 0

Reorder the terms:
dxy + 2dxy + 4dxy3 = 0

Combine like terms: dxy + 2dxy = 3dxy
3dxy + 4dxy3 = 0

Solving
3dxy + 4dxy3 = 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), 'dxy'.
dxy(3 + 4y2) = 0


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

Simplifying
dxy = 0

Solving
dxy = 0

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

Simplifying
dxy = 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 '(3 + 4y2)' equal to zero and attempt to solve:

Simplifying
3 + 4y2 = 0

Solving
3 + 4y2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4y2 = 0 + -3
4y2 = 0 + -3

Combine like terms: 0 + -3 = -3
4y2 = -3

Add '-4y2' to each side of the equation.
4y2 + -4y2 = -3 + -4y2

Combine like terms: 4y2 + -4y2 = 0
0 = -3 + -4y2

Simplifying
0 = -3 + -4y2

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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