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

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


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

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

Reorder the terms:
(dx2y + 1dy) = (1 + xy) * dx
(dx2y + 1dy) = (1 + xy) * dx

Reorder the terms for easier multiplication:
dx2y + 1dy = dx(1 + xy)
dx2y + 1dy = (1 * dx + xy * dx)
dx2y + 1dy = (1dx + dx2y)

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

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

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

Solving
1dy = 1dx

Solving for variable 'd'.

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

Add '-1dx' to each side of the equation.
-1dx + 1dy = 1dx + -1dx

Combine like terms: 1dx + -1dx = 0
-1dx + 1dy = 0

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


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

Simplifying
d = 0

Solving
d = 0

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

Simplifying
d = 0

Subproblem 2
Set the factor '(-1x + y)' equal to zero and attempt to solve:

Simplifying
-1x + y = 0

Solving
-1x + y = 0

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

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

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

Add '-1y' to each side of the equation.
y + -1y = x + -1y

Combine like terms: y + -1y = 0
0 = x + -1y

Simplifying
0 = x + -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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