Second Order DE with undefined constants

http://img220.imageshack.us/img220/7215/70427339.png

Hi guys,

May I obtain any hints on how to approach this question?

My class has not covered Legendre and Chebyshev polynomials, but after trying to do some research on the net I came across these which are similar to my question.

My current approach has been that this equation is similar to Euler form and so a possible solution is$\displaystyle y_{1} = x$.

From here use a reduction of order to obtain a second solution?

I am finding it difficult due to the arbitrary constants.

Any feedback would be greatly appreciated!!

Linda

Re: Second Order DE with undefined constants

The general solution has LegendreP and LegendreQ polynomials. I would investigate some special cases, like k = 0, or lambda = 0, and see what you get then. Also note that the LegendreP functions already are polynomials. The LegendreQ functions have other functions like logarithms inside them.

Re: Second Order DE with undefined constants

Hi Ackbeet,

Thank you very much for guiding me on the correct path, especially the hint about lambda =0.

I am now approaching this question via a series solution

Thank you!!!

Re: Second Order DE with undefined constants

You're welcome. Have a good one!