(D^4+13D^2+36)y=0

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Solution for (D^4+13D^2+36)y=0 equation: 


Simplifying
(D4 + 13D2 + 36) * y = 0

Reorder the terms:
(36 + 13D2 + D4) * y = 0

Reorder the terms for easier multiplication:
y(36 + 13D2 + D4) = 0
(36 * y + 13D2 * y + D4 * y) = 0
(36y + 13yD2 + yD4) = 0

Solving
36y + 13yD2 + yD4 = 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(36 + 13D2 + D4) = 0

Factor a trinomial.
y((9 + D2)(4 + D2)) = 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 '(9 + D2)' equal to zero and attempt to solve:

Simplifying
9 + D2 = 0

Solving
9 + D2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + D2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + D2 = 0 + -9
D2 = 0 + -9

Combine like terms: 0 + -9 = -9
D2 = -9

Add '-1D2' to each side of the equation.
D2 + -1D2 = -9 + -1D2

Combine like terms: D2 + -1D2 = 0
0 = -9 + -1D2

Simplifying
0 = -9 + -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 '(4 + D2)' equal to zero and attempt to solve:

Simplifying
4 + D2 = 0

Solving
4 + D2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + D2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + D2 = 0 + -4
D2 = 0 + -4

Combine like terms: 0 + -4 = -4
D2 = -4

Add '-1D2' to each side of the equation.
D2 + -1D2 = -4 + -1D2

Combine like terms: D2 + -1D2 = 0
0 = -4 + -1D2

Simplifying
0 = -4 + -1D2

The solution to this equation could not be determined.

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

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