((x^2)+4)dy+(e^2y)dx=0

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Solution for ((x^2)+4)dy+(e^2y)dx=0 equation: 


Simplifying
((x2) + 4) * dy + (e2y) * dx = 0
(x2 + 4) * dy + (e2y) * dx = 0

Reorder the terms:
(4 + x2) * dy + (e2y) * dx = 0

Reorder the terms for easier multiplication:
dy(4 + x2) + (e2y) * dx = 0
(4 * dy + x2 * dy) + (e2y) * dx = 0

Reorder the terms:
(dx2y + 4dy) + (e2y) * dx = 0
(dx2y + 4dy) + (e2y) * dx = 0

Multiply e2y * dx
dx2y + 4dy + de2xy = 0

Reorder the terms:
de2xy + dx2y + 4dy = 0

Solving
de2xy + dx2y + 4dy = 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(e2x + x2 + 4) = 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 '(e2x + x2 + 4)' equal to zero and attempt to solve:

Simplifying
e2x + x2 + 4 = 0

Reorder the terms:
4 + e2x + x2 = 0

Solving
4 + e2x + x2 = 0

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

Add '-4' to each side of the equation.
4 + e2x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + e2x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + e2x + x2 = 0 + -4
e2x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
e2x + x2 = -4

Add '-1e2x' to each side of the equation.
e2x + -1e2x + x2 = -4 + -1e2x

Combine like terms: e2x + -1e2x = 0
0 + x2 = -4 + -1e2x
x2 = -4 + -1e2x

Add '-1x2' to each side of the equation.
x2 + -1x2 = -4 + -1e2x + -1x2

Combine like terms: x2 + -1x2 = 0
0 = -4 + -1e2x + -1x2

Simplifying
0 = -4 + -1e2x + -1x2

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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