Homework Help: Differntial Equations

Firepanda · Apr 30, 2008

http://img231.imageshack.us/img231/5213/njtd7.jpg [Broken]

What order differential equation is this?

In my notes i have the 2nd order differntial 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 · Apr 30, 2008

[tex]\frac{d^2\theta}{dt^2}+\frac{d\theta}{dt}+sin\theta=0[/tex]

[tex]\frac{d^2\theta}{dt^2}+\frac{d\theta}{dt}=-sin\theta[/tex]

All solutions are of the form [itex]\theta=e^{rt}[/itex]

So the auxiliary equation is [itex]r^2+r=0 \Rightarrow r(r+1)=[/itex]

so the roots are r=0,-1

So the Complimentary function would be [itex]\theta=c_1+c_2e^{-t}[/itex]

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Homework Help: Differntial Equations

Firepanda

rock.freak667