# Thread: Second Order DE with undefined constants

1. ## 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$\displaystyle y_{1} = x$.

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

2. ## 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.

3. ## 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!!!

4. ## Re: Second Order DE with undefined constants

You're welcome. Have a good one!