ey=e^2x

Solution for ey=e^2x equation:

Simplifying
ey = e2x

Solving
ey = e2x

Solving for variable 'e'.

Combine like terms: e2x + -1e2x = 0
ey + -1e2x = 0

Factor out the Greatest Common Factor (GCF), 'e'.
e(y + -1ex) = 0

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

Simplifying
e = 0

Solving
e = 0

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

Simplifying
e = 0
Subproblem 2
Set the factor '(y + -1ex)' equal to zero and attempt to solve:

Simplifying
y + -1ex = 0

Reorder the terms:
-1ex + y = 0

Solving
-1ex + y = 0

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

Add '-1y' to each side of the equation.
-1ex + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
-1ex + 0 = 0 + -1y
-1ex = 0 + -1y
Remove the zero:
-1ex = -1y

Divide each side by '-1x'.
e = x-1y

Simplifying
e = x-1y
Solution
e = {0, x-1y}