# Homework Help: Solving a third order DE with Maple

1. Jul 30, 2009

### ehilge

1. The problem statement, all variables and given/known data
This problem relates to using a numerical analysis program called Maple. My question is not related to how to run the program, but the appropriate steps needed to solve the equation. So even if you aren't familiar with the program, please try to help me out.

Consider the third order non-linear differential equation: (y'')(y''')=y

a) Solve this equation in Maple.

b) Find all polynomial soltions y(x)= a0 + a1x + a2x2 + ... a5x5 of this equation (It turns out that these are all solutions that are polynomial)

2. Relevant equations
none that I'm aware of at this point

3. The attempt at a solution
a) the output from Maple is shown in the attached screenshot

b) I have thought over this for awhile and I cant think of a good methods to finding the polynomials. The only ways I have been taught to solve a high order DE is through reduction of order, which is impossible since I don't have a solution I can work with. And variation of parameters, which I can't see working very well. Also, I'm thinking that the solution to (b) might have something to do with interpreting the solution found in (a) since there is a polynomial part in there. But again, I don't see how to create a polynomial solution out of it. So, any ideas on how to find the polynomial solutions, and particularly what steps I could take with the computer to get there?
thanks!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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