(3e^3x(y)-2x)dx+e^3x(dy)=0

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Solution for (3e^3x(y)-2x)dx+e^3x(dy)=0 equation: 


Simplifying
(3e3x(y) + -2x) * dx + e3x(dy) = 0

Multiply e3x * y
(3e3xy + -2x) * dx + e3x(dy) = 0

Reorder the terms for easier multiplication:
dx(3e3xy + -2x) + e3x(dy) = 0
(3e3xy * dx + -2x * dx) + e3x(dy) = 0
(3de3x2y + -2dx2) + e3x(dy) = 0

Multiply e3x * dy
3de3x2y + -2dx2 + de3xy = 0

Reorder the terms:
de3xy + 3de3x2y + -2dx2 = 0

Solving
de3xy + 3de3x2y + -2dx2 = 0

Solving for variable 'd'.

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

Factor out the Greatest Common Factor (GCF), 'dx'.
dx(e3y + 3e3xy + -2x) = 0


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

Simplifying
dx = 0

Solving
dx = 0

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

Simplifying
dx = 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 '(e3y + 3e3xy + -2x)' equal to zero and attempt to solve:

Simplifying
e3y + 3e3xy + -2x = 0

Reorder the terms:
3e3xy + e3y + -2x = 0

Solving
3e3xy + e3y + -2x = 0

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

Add '-3e3xy' to each side of the equation.
3e3xy + e3y + -3e3xy + -2x = 0 + -3e3xy

Reorder the terms:
3e3xy + -3e3xy + e3y + -2x = 0 + -3e3xy

Combine like terms: 3e3xy + -3e3xy = 0
0 + e3y + -2x = 0 + -3e3xy
e3y + -2x = 0 + -3e3xy
Remove the zero:
e3y + -2x = -3e3xy

Add '-1e3y' to each side of the equation.
e3y + -1e3y + -2x = -3e3xy + -1e3y

Combine like terms: e3y + -1e3y = 0
0 + -2x = -3e3xy + -1e3y
-2x = -3e3xy + -1e3y

Add '2x' to each side of the equation.
-2x + 2x = -3e3xy + -1e3y + 2x

Combine like terms: -2x + 2x = 0
0 = -3e3xy + -1e3y + 2x

Simplifying
0 = -3e3xy + -1e3y + 2x

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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