(x)dx+(5y^4+3)dy=0

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Solution for (x)dx+(5y^4+3)dy=0 equation: 


Simplifying
(x) * dx + (5y4 + 3) * dy = 0

Multiply x * dx
dx2 + (5y4 + 3) * dy = 0

Reorder the terms:
dx2 + (3 + 5y4) * dy = 0

Reorder the terms for easier multiplication:
dx2 + dy(3 + 5y4) = 0
dx2 + (3 * dy + 5y4 * dy) = 0
dx2 + (3dy + 5dy5) = 0

Solving
dx2 + 3dy + 5dy5 = 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(x2 + 3y + 5y5) = 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 '(x2 + 3y + 5y5)' equal to zero and attempt to solve:

Simplifying
x2 + 3y + 5y5 = 0

Solving
x2 + 3y + 5y5 = 0

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

Add '-1x2' to each side of the equation.
x2 + 3y + -1x2 + 5y5 = 0 + -1x2

Reorder the terms:
x2 + -1x2 + 3y + 5y5 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 3y + 5y5 = 0 + -1x2
3y + 5y5 = 0 + -1x2
Remove the zero:
3y + 5y5 = -1x2

Add '-3y' to each side of the equation.
3y + -3y + 5y5 = -1x2 + -3y

Combine like terms: 3y + -3y = 0
0 + 5y5 = -1x2 + -3y
5y5 = -1x2 + -3y

Add '-5y5' to each side of the equation.
5y5 + -5y5 = -1x2 + -3y + -5y5

Combine like terms: 5y5 + -5y5 = 0
0 = -1x2 + -3y + -5y5

Simplifying
0 = -1x2 + -3y + -5y5

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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