(y^2+1)dx+(4x*y*dy)=0

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


Simplifying
(y2 + 1) * dx + (4x * y * dy) = 0

Reorder the terms:
(1 + y2) * dx + (4x * y * dy) = 0

Reorder the terms for easier multiplication:
dx(1 + y2) + (4x * y * dy) = 0
(1 * dx + y2 * dx) + (4x * y * dy) = 0
(1dx + dxy2) + (4x * y * dy) = 0

Multiply x * y
1dx + dxy2 + (4xy * dy) = 0

Multiply xy * dy
1dx + dxy2 + (4dxy2) = 0

Combine like terms: dxy2 + (4dxy2) = 5dxy2
1dx + 5dxy2 = 0

Solving
1dx + 5dxy2 = 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(1 + 5y2) = 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 '(1 + 5y2)' equal to zero and attempt to solve:

Simplifying
1 + 5y2 = 0

Solving
1 + 5y2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5y2 = 0 + -1
5y2 = 0 + -1

Combine like terms: 0 + -1 = -1
5y2 = -1

Add '-5y2' to each side of the equation.
5y2 + -5y2 = -1 + -5y2

Combine like terms: 5y2 + -5y2 = 0
0 = -1 + -5y2

Simplifying
0 = -1 + -5y2

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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