(6y^2+1)dy=4dx

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Solution for (6y^2+1)dy=4dx equation: 


Simplifying
(6y2 + 1) * dy = 4dx

Reorder the terms:
(1 + 6y2) * dy = 4dx

Reorder the terms for easier multiplication:
dy(1 + 6y2) = 4dx
(1 * dy + 6y2 * dy) = 4dx
(1dy + 6dy3) = 4dx

Solving
1dy + 6dy3 = 4dx

Solving for variable 'd'.

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

Add '-4dx' to each side of the equation.
1dy + -4dx + 6dy3 = 4dx + -4dx

Reorder the terms:
-4dx + 1dy + 6dy3 = 4dx + -4dx

Combine like terms: 4dx + -4dx = 0
-4dx + 1dy + 6dy3 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(-4x + y + 6y3) = 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 '(-4x + y + 6y3)' equal to zero and attempt to solve:

Simplifying
-4x + y + 6y3 = 0

Solving
-4x + y + 6y3 = 0

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

Add '4x' to each side of the equation.
-4x + y + 4x + 6y3 = 0 + 4x

Reorder the terms:
-4x + 4x + y + 6y3 = 0 + 4x

Combine like terms: -4x + 4x = 0
0 + y + 6y3 = 0 + 4x
y + 6y3 = 0 + 4x
Remove the zero:
y + 6y3 = 4x

Add '-1y' to each side of the equation.
y + -1y + 6y3 = 4x + -1y

Combine like terms: y + -1y = 0
0 + 6y3 = 4x + -1y
6y3 = 4x + -1y

Add '-6y3' to each side of the equation.
6y3 + -6y3 = 4x + -1y + -6y3

Combine like terms: 6y3 + -6y3 = 0
0 = 4x + -1y + -6y3

Simplifying
0 = 4x + -1y + -6y3

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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