(12e^2x)(y^2-y)dx=dy

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Solution for (12e^2x)(y^2-y)dx=dy equation: 


Simplifying
(12e2x)(y2 + -1y) * dx = dy

Remove parenthesis around (12e2x)
12e2x(y2 + -1y) * dx = dy

Reorder the terms:
12e2x(-1y + y2) * dx = dy

Reorder the terms for easier multiplication:
12e2x * dx(-1y + y2) = dy

Multiply e2x * dx
12de2x2(-1y + y2) = dy
(-1y * 12de2x2 + y2 * 12de2x2) = dy
(-12de2x2y + 12de2x2y2) = dy

Solving
-12de2x2y + 12de2x2y2 = dy

Solving for variable 'd'.

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

Add '-1dy' to each side of the equation.
-12de2x2y + 12de2x2y2 + -1dy = dy + -1dy

Combine like terms: dy + -1dy = 0
-12de2x2y + 12de2x2y2 + -1dy = 0

Factor out the Greatest Common Factor (GCF), 'dy'.
dy(-12e2x2 + 12e2x2y + -1) = 0


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

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-12e2x2 + 12e2x2y + -1)' equal to zero and attempt to solve:

Simplifying
-12e2x2 + 12e2x2y + -1 = 0

Reorder the terms:
-1 + -12e2x2 + 12e2x2y = 0

Solving
-1 + -12e2x2 + 12e2x2y = 0

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

Add '1' to each side of the equation.
-1 + -12e2x2 + 1 + 12e2x2y = 0 + 1

Reorder the terms:
-1 + 1 + -12e2x2 + 12e2x2y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -12e2x2 + 12e2x2y = 0 + 1
-12e2x2 + 12e2x2y = 0 + 1

Combine like terms: 0 + 1 = 1
-12e2x2 + 12e2x2y = 1

Add '12e2x2' to each side of the equation.
-12e2x2 + 12e2x2 + 12e2x2y = 1 + 12e2x2

Combine like terms: -12e2x2 + 12e2x2 = 0
0 + 12e2x2y = 1 + 12e2x2
12e2x2y = 1 + 12e2x2

Add '-12e2x2y' to each side of the equation.
12e2x2y + -12e2x2y = 1 + 12e2x2 + -12e2x2y

Combine like terms: 12e2x2y + -12e2x2y = 0
0 = 1 + 12e2x2 + -12e2x2y

Simplifying
0 = 1 + 12e2x2 + -12e2x2y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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