I'm stuck with these three ODEs:

Nothing I tried worked, could you please help me? A hint on which method to try would be really great.

Thank you!

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- September 27th 2008, 12:49 PMmarianneI need help with 3 ODEs.
I'm stuck with these three ODEs:

Nothing I tried worked, could you please help me? A hint on which method to try would be really great.

Thank you! - September 27th 2008, 01:22 PMmarianne
The second one is Bessel's equation, I think. I'll Google for the solution.

If anyone has an idea for the other two.. - September 27th 2008, 01:31 PMJhevon
- September 27th 2008, 01:39 PMmarianne
I've found that Euler equation has the form:

, but I don't have a**constant**times y, but something dependent on x..?

Edit: I thought you were talking about the first one, sorry. :-(

Also, we haven't done series solutions in class yet, but I'll try to Google it. Thank you. - September 27th 2008, 01:45 PMJhevon
- September 27th 2008, 01:51 PMmarianne
Yes, I know, I edited the post above, I thought you were talking about the first one. It's not an excuse, but it's late in this timezone. :-)

Quote:

i will think of other ways to do the problems. if you haven't done series solutions, it would be a lot to learn just to do these. so you probably aren't expected to do them that way

- September 27th 2008, 01:57 PMmarianne
I solved the second one. In case someone has a similar problem, I've found this page Pauls Online Notes : Differential Equations - Euler Equations to be useful.

- September 27th 2008, 02:55 PMNonCommAlg
- September 28th 2008, 12:37 AMmarianne
Thank you so much!!!

- September 28th 2008, 12:57 AMbkarpuzEuler type.
Euler type equations have polynomial type solutions.

Just substitute and get a parabola of , solve it and get two roots and (this is for second-order equations, for higher-order equations you get polynomial of degree ).

Then, the solution is

where and are arbitrary constants.

**Note.**Note that will decrease the power of by while the factor will increase it by , hence you will get for any .

This is why we search solutions of polynomial type.