(D^2-5D+6)y=0,y(0)=0,y(0)=0

Solution for (D^2-5D+6)y=0,y(0)=0,y(0)=0 equation:

(^2-5+6)D=0.D(0)=0.D(0)=0

We move all terms to the left:

(^2-5+6)D-(0.D(0))=0

We add all the numbers together, and all the variables

(^2-5+6)D-0=0

We add all the numbers together, and all the variables

(^2-5+6)D=0

We multiply parentheses

D^2-5D+6D=0

We add all the numbers together, and all the variables

D^2+D=0

a = 1; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·1·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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