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

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


Simplifying
(x4 + 2y)(dy) + -1x(dx) = 0

Reorder the terms for easier multiplication:
dy(x4 + 2y) + -1x(dx) = 0
(x4 * dy + 2y * dy) + -1x(dx) = 0
(dx4y + 2dy2) + -1x(dx) = 0

Multiply x * dx
dx4y + 2dy2 + -1dx2 = 0

Reorder the terms:
-1dx2 + dx4y + 2dy2 = 0

Solving
-1dx2 + dx4y + 2dy2 = 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(-1x2 + x4y + 2y2) = 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 '(-1x2 + x4y + 2y2)' equal to zero and attempt to solve:

Simplifying
-1x2 + x4y + 2y2 = 0

Solving
-1x2 + x4y + 2y2 = 0

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

Add 'x2' to each side of the equation.
-1x2 + x4y + x2 + 2y2 = 0 + x2

Reorder the terms:
-1x2 + x2 + x4y + 2y2 = 0 + x2

Combine like terms: -1x2 + x2 = 0
0 + x4y + 2y2 = 0 + x2
x4y + 2y2 = 0 + x2
Remove the zero:
x4y + 2y2 = x2

Add '-1x4y' to each side of the equation.
x4y + -1x4y + 2y2 = x2 + -1x4y

Combine like terms: x4y + -1x4y = 0
0 + 2y2 = x2 + -1x4y
2y2 = x2 + -1x4y

Add '-2y2' to each side of the equation.
2y2 + -2y2 = x2 + -1x4y + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = x2 + -1x4y + -2y2

Simplifying
0 = x2 + -1x4y + -2y2

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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