dy*y^2=(x-5)*dx

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


Simplifying
dy * y2 = (x + -5) * dx

Multiply dy * y2
dy3 = (x + -5) * dx

Reorder the terms:
dy3 = (-5 + x) * dx

Reorder the terms for easier multiplication:
dy3 = dx(-5 + x)
dy3 = (-5 * dx + x * dx)
dy3 = (-5dx + dx2)

Solving
dy3 = -5dx + dx2

Solving for variable 'd'.

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

Add '5dx' to each side of the equation.
5dx + dy3 = -5dx + 5dx + dx2

Combine like terms: -5dx + 5dx = 0
5dx + dy3 = 0 + dx2
5dx + dy3 = dx2

Add '-1dx2' to each side of the equation.
5dx + -1dx2 + dy3 = dx2 + -1dx2

Combine like terms: dx2 + -1dx2 = 0
5dx + -1dx2 + dy3 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(5x + -1x2 + y3) = 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 + -1x2 + y3)' equal to zero and attempt to solve:

Simplifying
5x + -1x2 + y3 = 0

Solving
5x + -1x2 + y3 = 0

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

Add '-5x' to each side of the equation.
5x + -1x2 + -5x + y3 = 0 + -5x

Reorder the terms:
5x + -5x + -1x2 + y3 = 0 + -5x

Combine like terms: 5x + -5x = 0
0 + -1x2 + y3 = 0 + -5x
-1x2 + y3 = 0 + -5x
Remove the zero:
-1x2 + y3 = -5x

Add 'x2' to each side of the equation.
-1x2 + x2 + y3 = -5x + x2

Combine like terms: -1x2 + x2 = 0
0 + y3 = -5x + x2
y3 = -5x + x2

Add '-1y3' to each side of the equation.
y3 + -1y3 = -5x + x2 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -5x + x2 + -1y3

Simplifying
0 = -5x + x2 + -1y3

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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