(D^4-81)y=0

Solution for (D^4-81)y=0 equation:

(^4-81)D=0

We multiply parentheses

D^2-81D=0

a = 1; b = -81; c = 0;
Δ = b2-4ac
Δ = -812-4·1·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-81}{2*1}=\frac{0}{2}
=0
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+81}{2*1}=\frac{162}{2}
=81
$