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

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


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

Reorder the terms for easier multiplication:
dx(12e2x + -1y) = dy
(12e2x * dx + -1y * dx) = dy
(12de2x2 + -1dxy) = dy

Solving
12de2x2 + -1dxy = 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.
12de2x2 + -1dxy + -1dy = dy + -1dy

Combine like terms: dy + -1dy = 0
12de2x2 + -1dxy + -1dy = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(12e2x2 + -1xy + -1y) = 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 '(12e2x2 + -1xy + -1y)' equal to zero and attempt to solve:

Simplifying
12e2x2 + -1xy + -1y = 0

Solving
12e2x2 + -1xy + -1y = 0

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

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

Reorder the terms:
12e2x2 + -12e2x2 + -1xy + -1y = 0 + -12e2x2

Combine like terms: 12e2x2 + -12e2x2 = 0
0 + -1xy + -1y = 0 + -12e2x2
-1xy + -1y = 0 + -12e2x2
Remove the zero:
-1xy + -1y = -12e2x2

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

Combine like terms: -1xy + xy = 0
0 + -1y = -12e2x2 + xy
-1y = -12e2x2 + xy

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

Combine like terms: -1y + y = 0
0 = -12e2x2 + xy + y

Simplifying
0 = -12e2x2 + xy + y

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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