(x^2+y^2-5)dx=(y+xy)dy

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Solution for (x^2+y^2-5)dx=(y+xy)dy equation: 


Simplifying
(x2 + y2 + -5) * dx = (y + xy) * dy

Reorder the terms:
(-5 + x2 + y2) * dx = (y + xy) * dy

Reorder the terms for easier multiplication:
dx(-5 + x2 + y2) = (y + xy) * dy
(-5 * dx + x2 * dx + y2 * dx) = (y + xy) * dy

Reorder the terms:
(-5dx + dxy2 + dx3) = (y + xy) * dy
(-5dx + dxy2 + dx3) = (y + xy) * dy

Reorder the terms:
-5dx + dxy2 + dx3 = (xy + y) * dy

Reorder the terms for easier multiplication:
-5dx + dxy2 + dx3 = dy(xy + y)
-5dx + dxy2 + dx3 = (xy * dy + y * dy)
-5dx + dxy2 + dx3 = (dxy2 + dy2)

Add '-1dxy2' to each side of the equation.
-5dx + dxy2 + -1dxy2 + dx3 = dxy2 + -1dxy2 + dy2

Combine like terms: dxy2 + -1dxy2 = 0
-5dx + 0 + dx3 = dxy2 + -1dxy2 + dy2
-5dx + dx3 = dxy2 + -1dxy2 + dy2

Combine like terms: dxy2 + -1dxy2 = 0
-5dx + dx3 = 0 + dy2
-5dx + dx3 = dy2

Solving
-5dx + dx3 = 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.
-5dx + dx3 + -1dy2 = dy2 + -1dy2

Combine like terms: dy2 + -1dy2 = 0
-5dx + dx3 + -1dy2 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(-5x + x3 + -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 '(-5x + x3 + -1y2)' equal to zero and attempt to solve:

Simplifying
-5x + x3 + -1y2 = 0

Solving
-5x + x3 + -1y2 = 0

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

Add '5x' to each side of the equation.
-5x + x3 + 5x + -1y2 = 0 + 5x

Reorder the terms:
-5x + 5x + x3 + -1y2 = 0 + 5x

Combine like terms: -5x + 5x = 0
0 + x3 + -1y2 = 0 + 5x
x3 + -1y2 = 0 + 5x
Remove the zero:
x3 + -1y2 = 5x

Add '-1x3' to each side of the equation.
x3 + -1x3 + -1y2 = 5x + -1x3

Combine like terms: x3 + -1x3 = 0
0 + -1y2 = 5x + -1x3
-1y2 = 5x + -1x3

Add 'y2' to each side of the equation.
-1y2 + y2 = 5x + -1x3 + y2

Combine like terms: -1y2 + y2 = 0
0 = 5x + -1x3 + y2

Simplifying
0 = 5x + -1x3 + 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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