# Higher Order ODES

1. Mar 16, 2015

### mshiddensecret

1. The problem statement, all variables and given/known data

y''''''+y'''=t

2. Relevant equations

3. The attempt at a solution

I got all the roots and solved the homo eq.

Then I tried to guess the partial eq and got At+B

However, I don't know how to proceed because the 6th derivative or the 3rd would be 0.

2. Mar 16, 2015

### SteamKing

Staff Emeritus
I think you mean, you tried to guess the particular solution and got At + B

It's not clear why you guessed yp = At + B, since the highest order derivative is 6. This implies that yp should be a 7th degree polynomial.

3. Mar 16, 2015

### LCKurtz

You don't need a 7th degree polynomial for $y_p$ for this problem. Try $y_p = Ct^4$.

4. Mar 18, 2015

### Ray Vickson

Mod note: removed a quote that was too much help.

You can also let $z(t) = y'''(t)$ and write the DE as $(z(t) - t)''' + (z(t)-t) = 0$, which is homogeneous of degree 3 in $z(t)-t$. After finding $z(t)$, integrating three times (with constants of integration included) will get $y(t)$.

Last edited by a moderator: Mar 18, 2015
5. Mar 18, 2015

### haruspex

It only implies the general solution will be of degree 5, no? The degree of the particular solution will often be the sum of the least degree of differentiation and the highest degree of the polynomial on the other side of the equation. In this case, 3+1=4.