Understanding Second Order Homogeneous Differential Equations

[Firepanda]

http://img231.imageshack.us/img231/5213/njtd7.jpg

What order differential equation is this?

In my notes i have the 2nd order differential equation (homogeneous equation) as

y'' + py' + qy = 0

I take possible soultions in the form y = e^mx

=> (m^2 + pm + q)e^mx = 0

Then I take solutions of the equation using the quadratic forumula of m^2 + pm + q = 0?

General soultion is then y = c(1)y(1) + c(2)y(2)

Am I getting this right?

Thanks!

here do p and q both equal to 1?

 

[rock.freak667]

$$\frac{d^2\theta}{dt^2}+\frac{d\theta}{dt}+sin\theta=0$$

$$\frac{d^2\theta}{dt^2}+\frac{d\theta}{dt}=-sin\theta$$

All solutions are of the form $\theta=e^{rt}$

So the auxiliary equation is $r^2+r=0 \Rightarrow r(r+1)=$

so the roots are r=0,-1

So the Complimentary function would be $\theta=c_1+c_2e^{-t}$