# Homogeneous Linear DE's - solving IVP's

1. Sep 30, 2009

### tatiana_eggs

Homogeneous Linear DE's -- solving IVP's

1. The problem statement, all variables and given/known data

Solve the given IVP:

d^2y/dt^2 - 4 dy/dt -5y = 0; y(1)=0, y'(1)=2

2. Relevant equations

N/A

3. The attempt at a solution

I've solved and got the general solution y=c1e5t+c2e-t

I'm plugging in the following to solve for my two constants:

y(1)=0=c1e5+c2/e

y'(1)=2=5c1e5-c2e

So I have a system of 2 linear equations, and I can just add the two together and get:

2=6c1e5

and solving for c1 = e5/3

I would go on and solve for c2, but I checked the back of the book and they have:

y = 1/3e5(t-1)-1/3e-(t-1)

How did they get c1 = 1/3 and e5(t-1) ?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 30, 2009

### tiny-tim

Hi tatiana_eggs!
erm … c1 = e-5/3 …

which gives the 1/3e5(t-1) in the book.

3. Sep 30, 2009

### tatiana_eggs

Re: Homogeneous Linear DE's -- solving IVP's

Oh my gosh... duh.. I seem to be slowly losing my algebra skills as I learn more and more math.

Thanks so much!