Thread: differential equation help

OK. I'm working on a homework problem in Diffy Equ. and I'm stuck halfway through. It is a homogenius equation w/ constant coefficients.

y'''-8y''-y'+8y=0

y(0)=-7, y'(0)=7, y''(0)=-7

I've gotten as far as:

y= C1e^x+C2e^-x+C3e^-8x
y'= C1e^x+c2e^-x-8C3e^-8x
y''= C1e^x+C2e^-x+64C3e^-8x

c1+c2+c3=-7
c1+c2-8c3=7
c1+c2+64c3=-7

I'm getting stuck on solving for c1 c2 and c3 which I guess is more algebra than anything. If someone could walk me this it would be great. I was using substitution. After I get this I can do the rest.

Thanks

Originally Posted by tinkerbell03815

OK. I'm working on a homework problem in Diffy Equ. and I'm stuck halfway through. It is a homogenius equation w/ constant coefficients.

y'''-8y''-y'+8y=0

y(0)=-7, y'(0)=7, y''(0)=-7

I've gotten as far as:

y= C1e^x+C2e^-x+C3e^-8x
y'= C1e^x+c2e^-x-8C3e^-8x
y''= C1e^x+C2e^-x+64C3e^-8x

c1+c2+c3=-7
c1+c2-8c3=7
c1+c2+64c3=-7

I'm getting stuck on solving for c1 c2 and c3 which I guess is more algebra than anything. If someone could walk me this it would be great. I was using substitution. After I get this I can do the rest.

Thanks

Check your derivatives. Especially the sign on the second term.

-Dan

Thanks, I got it. I knew I was making some kind of stupid mistake