(D^4-49)y=0

Solution for (D^4-49)y=0 equation:

(^4-49)D=0

We multiply parentheses

D^2-49D=0

a = 1; b = -49; c = 0;
Δ = b2-4ac
Δ = -492-4·1·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-49}{2*1}=\frac{0}{2}
=0
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+49}{2*1}=\frac{98}{2}
=49
$