00:01
In this problem, we are given the following differential equation.
00:03
We have 4y' ' plus 4y ' plus 6y equal to 0.
00:12
From here, we are going to get the characteristic equation.
00:15
The characteristic equation for this differential equation will be as follows.
00:24
It will be 4r squared plus 4r plus 6 equal to 0.
00:30
Next, we will use the quadratic formula.
00:35
So using the quadratic formula, using the quadratic formula to solve for this quadratic equation, we are going to get r equals, remember, negative b plus minus the square root of b squared minus 4ac and then all over 2 times a.
00:58
So in our case, we get r equals negative 4 plus or minus the square root of 4 squared, which is 16, minus 4 times a, which is 4, times c, where c is 6, and then all over 2 times 4.
01:18
So 2 times 4 is 8.
01:20
So we're going to have r equals as the following here.
01:25
We're going to have negative 4 plus or minus...