Thread: 4th order differential equation??

d4y/dx4 - 8( d2y/dx2) + 16y = 0

This is on one of my '2nd order differential equations' problem sheets and its a of fourth order leaving me a bit confused. Ive tried reducing the order but I cant get it. Is there a rule/theorem Ive missed??

A helping hand would be greatly appreciated

Nappy

Why do you need to reduce it?

1) Create a system z = d2y/dx2. What does that do after some substitution?

2) Factor the characteristic polynomial in ignorance ==> I didn't even notice it wasn't second degree! Just see what happens.

Yea I tried that method and it was fine for the first 2 terms but I didnt know what to do with the 16y term, integrating twice seems a bit messy??

so i get

z'' -8z + 16y= 0

How to convert the y value??

Did you factor the Characteristic Polynomial? That's a great place to start.