(D^6+2D^4+D^2)y=0

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Solution for (D^6+2D^4+D^2)y=0 equation: 


Simplifying
(D6 + 2D4 + D2) * y = 0

Reorder the terms:
(D2 + 2D4 + D6) * y = 0

Reorder the terms for easier multiplication:
y(D2 + 2D4 + D6) = 0
(D2 * y + 2D4 * y + D6 * y) = 0
(yD2 + 2yD4 + yD6) = 0

Solving
yD2 + 2yD4 + 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), 'yD2'.
yD2(1 + 2D2 + D4) = 0

Factor a trinomial.
yD2((1 + D2)(1 + D2)) = 0


Subproblem 1
Set the factor 'yD2' equal to zero and attempt to solve:

Simplifying
yD2 = 0

Solving
yD2 = 0

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

Simplifying
yD2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(1 + D2)' equal to zero and attempt to solve:

Simplifying
1 + D2 = 0

Solving
1 + D2 = 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 + D2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + D2 = 0 + -1
D2 = 0 + -1

Combine like terms: 0 + -1 = -1
D2 = -1

Add '-1D2' to each side of the equation.
D2 + -1D2 = -1 + -1D2

Combine like terms: D2 + -1D2 = 0
0 = -1 + -1D2

Simplifying
0 = -1 + -1D2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(1 + D2)' equal to zero and attempt to solve:

Simplifying
1 + D2 = 0

Solving
1 + D2 = 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 + D2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + D2 = 0 + -1
D2 = 0 + -1

Combine like terms: 0 + -1 = -1
D2 = -1

Add '-1D2' to each side of the equation.
D2 + -1D2 = -1 + -1D2

Combine like terms: D2 + -1D2 = 0
0 = -1 + -1D2

Simplifying
0 = -1 + -1D2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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