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differential equation


Mathematica does not support the solutions of differential equations 
of the form
      
	g(x)f'' + g (x)f' + a f  = 0
         2   n     1    n    n n

particularly Legendre differential equations even though orthogonal
polynomials are built into the kernel.  Is there any particular reason
for this ?

I tried ( among others )

DSolve[(1-x^2) y''[x] - 2x y'[x] + n(n+1) y[x] == 0, y[x], x]

which returned unevaluated. The result should be
 
y = c[1] LegendreP[n, x] + c[2] LegendreQ[n, x].

Does someone have any idea what is going on ?


H. I. SALEH
salehh at jacobs.cs.orst.edu





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