Homogeneous Linear DE's - solving IVP's

[tatiana_eggs]

Homogeneous Linear DE's -- solving IVP's

Homework Statement

Solve the given IVP:

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

Homework Equations

N/A

The Attempt at a Solution

I've solved and got the general solution y=c₁e^5t+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 = 1/3e^5(t-1)-1/3e^-(t-1)

How did they get c₁ = 1/3 and e^5(t-1) ?

 

[tiny-tim]

Hi tatiana_eggs!

2=6c₁e⁵

and solving for c₁ = e⁵/3

erm … c₁ = e^-5/3 …

which gives the 1/3e^5(t-1) in the book. ​

 

[tatiana_eggs]

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

Thanks so much!