Xdy-ydx=sqrt(x^2-y^2)dx

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Solution for Xdy-ydx=sqrt(x^2-y^2)dx equation: 


Simplifying
Xdy + -1ydx = sqrt(x2 + -1y2) * dx

Reorder the terms:
-1dxy + dyX = sqrt(x2 + -1y2) * dx

Reorder the terms for easier multiplication:
-1dxy + dyX = qrst * dx(x2 + -1y2)

Multiply qrst * dx
-1dxy + dyX = dqrstx(x2 + -1y2)
-1dxy + dyX = (x2 * dqrstx + -1y2 * dqrstx)

Reorder the terms:
-1dxy + dyX = (-1dqrstxy2 + dqrstx3)
-1dxy + dyX = (-1dqrstxy2 + dqrstx3)

Solving
-1dxy + dyX = -1dqrstxy2 + dqrstx3

Solving for variable 'd'.

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

Add 'dqrstxy2' to each side of the equation.
-1dxy + dqrstxy2 + dyX = -1dqrstxy2 + dqrstxy2 + dqrstx3

Reorder the terms:
dqrstxy2 + -1dxy + dyX = -1dqrstxy2 + dqrstxy2 + dqrstx3

Combine like terms: -1dqrstxy2 + dqrstxy2 = 0
dqrstxy2 + -1dxy + dyX = 0 + dqrstx3
dqrstxy2 + -1dxy + dyX = dqrstx3

Add '-1dqrstx3' to each side of the equation.
dqrstxy2 + -1dxy + -1dqrstx3 + dyX = dqrstx3 + -1dqrstx3

Reorder the terms:
dqrstxy2 + -1dqrstx3 + -1dxy + dyX = dqrstx3 + -1dqrstx3

Combine like terms: dqrstx3 + -1dqrstx3 = 0
dqrstxy2 + -1dqrstx3 + -1dxy + dyX = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(qrstxy2 + -1qrstx3 + -1xy + yX) = 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 '(qrstxy2 + -1qrstx3 + -1xy + yX)' equal to zero and attempt to solve:

Simplifying
qrstxy2 + -1qrstx3 + -1xy + yX = 0

Solving
qrstxy2 + -1qrstx3 + -1xy + yX = 0

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

Add '-1qrstxy2' to each side of the equation.
qrstxy2 + -1qrstx3 + -1xy + -1qrstxy2 + yX = 0 + -1qrstxy2

Reorder the terms:
qrstxy2 + -1qrstxy2 + -1qrstx3 + -1xy + yX = 0 + -1qrstxy2

Combine like terms: qrstxy2 + -1qrstxy2 = 0
0 + -1qrstx3 + -1xy + yX = 0 + -1qrstxy2
-1qrstx3 + -1xy + yX = 0 + -1qrstxy2
Remove the zero:
-1qrstx3 + -1xy + yX = -1qrstxy2

Add 'qrstx3' to each side of the equation.
-1qrstx3 + -1xy + qrstx3 + yX = -1qrstxy2 + qrstx3

Reorder the terms:
-1qrstx3 + qrstx3 + -1xy + yX = -1qrstxy2 + qrstx3

Combine like terms: -1qrstx3 + qrstx3 = 0
0 + -1xy + yX = -1qrstxy2 + qrstx3
-1xy + yX = -1qrstxy2 + qrstx3

Add 'xy' to each side of the equation.
-1xy + xy + yX = -1qrstxy2 + qrstx3 + xy

Combine like terms: -1xy + xy = 0
0 + yX = -1qrstxy2 + qrstx3 + xy
yX = -1qrstxy2 + qrstx3 + xy

Add '-1yX' to each side of the equation.
yX + -1yX = -1qrstxy2 + qrstx3 + xy + -1yX

Combine like terms: yX + -1yX = 0
0 = -1qrstxy2 + qrstx3 + xy + -1yX

Simplifying
0 = -1qrstxy2 + qrstx3 + xy + -1yX

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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