(xy)dx+(1+x^2)dy=0

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Solution for (xy)dx+(1+x^2)dy=0 equation: 


Simplifying
(xy) * dx + (1 + x2) * dy = 0

Multiply xy * dx
dx2y + (1 + x2) * dy = 0

Reorder the terms for easier multiplication:
dx2y + dy(1 + x2) = 0
dx2y + (1 * dy + x2 * dy) = 0

Reorder the terms:
dx2y + (dx2y + 1dy) = 0
dx2y + (dx2y + 1dy) = 0

Combine like terms: dx2y + dx2y = 2dx2y
2dx2y + 1dy = 0

Solving
2dx2y + 1dy = 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), 'dy'.
dy(2x2 + 1) = 0


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

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 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 '(2x2 + 1)' equal to zero and attempt to solve:

Simplifying
2x2 + 1 = 0

Reorder the terms:
1 + 2x2 = 0

Solving
1 + 2x2 = 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 + 2x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x2 = 0 + -1
2x2 = 0 + -1

Combine like terms: 0 + -1 = -1
2x2 = -1

Add '-2x2' to each side of the equation.
2x2 + -2x2 = -1 + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 = -1 + -2x2

Simplifying
0 = -1 + -2x2

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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