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

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


Simplifying
((x2) + 4) * dy + (e2) * dx = 0
(x2 + 4) * dy + (e2) * dx = 0

Reorder the terms:
(4 + x2) * dy + (e2) * dx = 0

Reorder the terms for easier multiplication:
dy(4 + x2) + (e2) * dx = 0
(4 * dy + x2 * dy) + (e2) * dx = 0

Reorder the terms:
(dx2y + 4dy) + (e2) * dx = 0
(dx2y + 4dy) + (e2) * dx = 0

Multiply e2 * dx
dx2y + 4dy + de2x = 0

Reorder the terms:
de2x + dx2y + 4dy = 0

Solving
de2x + 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), 'd'.
d(e2x + x2y + 4y) = 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 '(e2x + x2y + 4y)' equal to zero and attempt to solve:

Simplifying
e2x + x2y + 4y = 0

Solving
e2x + x2y + 4y = 0

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

Add '-1e2x' to each side of the equation.
e2x + x2y + -1e2x + 4y = 0 + -1e2x

Reorder the terms:
e2x + -1e2x + x2y + 4y = 0 + -1e2x

Combine like terms: e2x + -1e2x = 0
0 + x2y + 4y = 0 + -1e2x
x2y + 4y = 0 + -1e2x
Remove the zero:
x2y + 4y = -1e2x

Add '-1x2y' to each side of the equation.
x2y + -1x2y + 4y = -1e2x + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + 4y = -1e2x + -1x2y
4y = -1e2x + -1x2y

Add '-4y' to each side of the equation.
4y + -4y = -1e2x + -1x2y + -4y

Combine like terms: 4y + -4y = 0
0 = -1e2x + -1x2y + -4y

Simplifying
0 = -1e2x + -1x2y + -4y

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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