(1+y^2)*dx=y*dy

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


Simplifying
(1 + y2) * dx = y * dy

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

Multiply y * dy
1dx + dxy2 = dy2

Solving
1dx + dxy2 = dy2

Solving for variable 'd'.

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

Add '-1dy2' to each side of the equation.
1dx + dxy2 + -1dy2 = dy2 + -1dy2

Combine like terms: dy2 + -1dy2 = 0
1dx + dxy2 + -1dy2 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(x + xy2 + -1y2) = 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 '(x + xy2 + -1y2)' equal to zero and attempt to solve:

Simplifying
x + xy2 + -1y2 = 0

Solving
x + xy2 + -1y2 = 0

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

Add '-1x' to each side of the equation.
x + xy2 + -1x + -1y2 = 0 + -1x

Reorder the terms:
x + -1x + xy2 + -1y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + xy2 + -1y2 = 0 + -1x
xy2 + -1y2 = 0 + -1x
Remove the zero:
xy2 + -1y2 = -1x

Add '-1xy2' to each side of the equation.
xy2 + -1xy2 + -1y2 = -1x + -1xy2

Combine like terms: xy2 + -1xy2 = 0
0 + -1y2 = -1x + -1xy2
-1y2 = -1x + -1xy2

Add 'y2' to each side of the equation.
-1y2 + y2 = -1x + -1xy2 + y2

Combine like terms: -1y2 + y2 = 0
0 = -1x + -1xy2 + y2

Simplifying
0 = -1x + -1xy2 + y2

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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