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

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


Simplifying
(2xy + -1e2y) * dx + (x2 + xe2y + -1y) * dy = 0

Reorder the terms:
(-1e2y + 2xy) * dx + (x2 + xe2y + -1y) * dy = 0

Reorder the terms for easier multiplication:
dx(-1e2y + 2xy) + (x2 + xe2y + -1y) * dy = 0
(-1e2y * dx + 2xy * dx) + (x2 + xe2y + -1y) * dy = 0
(-1de2xy + 2dx2y) + (x2 + xe2y + -1y) * dy = 0

Reorder the terms:
-1de2xy + 2dx2y + (e2xy + x2 + -1y) * dy = 0

Reorder the terms for easier multiplication:
-1de2xy + 2dx2y + dy(e2xy + x2 + -1y) = 0
-1de2xy + 2dx2y + (e2xy * dy + x2 * dy + -1y * dy) = 0
-1de2xy + 2dx2y + (de2xy2 + dx2y + -1dy2) = 0

Reorder the terms:
-1de2xy + de2xy2 + 2dx2y + dx2y + -1dy2 = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
-1de2xy + de2xy2 + 3dx2y + -1dy2 = 0

Solving
-1de2xy + de2xy2 + 3dx2y + -1dy2 = 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), 'dy'.
dy(-1e2x + e2xy + 3x2 + -1y) = 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 '(-1e2x + e2xy + 3x2 + -1y)' equal to zero and attempt to solve:

Simplifying
-1e2x + e2xy + 3x2 + -1y = 0

Solving
-1e2x + e2xy + 3x2 + -1y = 0

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

Add 'e2x' to each side of the equation.
-1e2x + e2xy + 3x2 + e2x + -1y = 0 + e2x

Reorder the terms:
-1e2x + e2x + e2xy + 3x2 + -1y = 0 + e2x

Combine like terms: -1e2x + e2x = 0
0 + e2xy + 3x2 + -1y = 0 + e2x
e2xy + 3x2 + -1y = 0 + e2x
Remove the zero:
e2xy + 3x2 + -1y = e2x

Add '-1e2xy' to each side of the equation.
e2xy + 3x2 + -1e2xy + -1y = e2x + -1e2xy

Reorder the terms:
e2xy + -1e2xy + 3x2 + -1y = e2x + -1e2xy

Combine like terms: e2xy + -1e2xy = 0
0 + 3x2 + -1y = e2x + -1e2xy
3x2 + -1y = e2x + -1e2xy

Add '-3x2' to each side of the equation.
3x2 + -3x2 + -1y = e2x + -1e2xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + -1y = e2x + -1e2xy + -3x2
-1y = e2x + -1e2xy + -3x2

Add 'y' to each side of the equation.
-1y + y = e2x + -1e2xy + -3x2 + y

Combine like terms: -1y + y = 0
0 = e2x + -1e2xy + -3x2 + y

Simplifying
0 = e2x + -1e2xy + -3x2 + y

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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