(D^6+1)y=0

Solution for (D^6+1)y=0 equation:

Simplifying
(D6 + 1) * y = 0

Reorder the terms:
(1 + D6) * y = 0

Reorder the terms for easier multiplication:
y(1 + D6) = 0
(1 * y + D6 * y) = 0
(1y + yD6) = 0

Solving
1y + yD6 = 0

Solving for variable 'y'.

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

Factor out the Greatest Common Factor (GCF), 'y'.
y(1 + D6) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(1 + D6)' equal to zero and attempt to solve:

Simplifying
1 + D6 = 0

Solving
1 + D6 = 0

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

Add '-1' to each side of the equation.
1 + -1 + D6 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + D6 = 0 + -1
D6 = 0 + -1

Combine like terms: 0 + -1 = -1
D6 = -1

Add '-1D6' to each side of the equation.
D6 + -1D6 = -1 + -1D6

Combine like terms: D6 + -1D6 = 0
0 = -1 + -1D6

Simplifying
0 = -1 + -1D6

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}