Thread: Second Order DE with undefined constants

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 .

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

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.

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!!!

You're welcome. Have a good one!