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

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


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

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

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

Reorder the terms:
-1dx2y + -1dy + xy = 0

Solving
-1dx2y + -1dy + xy = 0

Solving for variable 'd'.

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

Add '-1xy' to each side of the equation.
-1dx2y + -1dy + xy + -1xy = 0 + -1xy

Combine like terms: xy + -1xy = 0
-1dx2y + -1dy + 0 = 0 + -1xy
-1dx2y + -1dy = 0 + -1xy
Remove the zero:
-1dx2y + -1dy = -1xy

Combine like terms: -1xy + xy = 0
-1dx2y + -1dy + xy = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1dx2 + -1d + x) = 0


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

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

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 '(-1dx2 + -1d + x)' equal to zero and attempt to solve:

Simplifying
-1dx2 + -1d + x = 0

Reorder the terms:
-1d + -1dx2 + x = 0

Solving
-1d + -1dx2 + x = 0

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

Add '-1x' to each side of the equation.
-1d + -1dx2 + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
-1d + -1dx2 + 0 = 0 + -1x
-1d + -1dx2 = 0 + -1x
Remove the zero:
-1d + -1dx2 = -1x

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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