# Thread: Homogeneous Equations with Constant Coefficients

1. ## Homogeneous Equations with Constant Coefficients

Find the general solution of the given differential equation.

y'' + 5y' = 0

The answer is y = C1 + C2*e^(-5t)

I don't know where to begin with this, unfortunately I missed this lecture. Thanks.

2. Originally Posted by pakman
Find the general solution of the given differential equation.

y'' + 5y' = 0

The answer is y = C1 + C2*e^(-5t)

I don't know where to begin with this, unfortunately I missed this lecture. Thanks.
The characheeristic equation:

k^2+5k=0

k(k+5)=0

k=0 or k=-5

Thus,

e^0 = 1 and e^{-5t} are solutions.

All linear combinators are,

C_1(1)+C_2*e^{-5t}