Why MATLAB sometimes cannot solve the relatively particular case but can solve the relatively general case?
I tried to input (x^2-1)*D2y + 0*x*Dy + 1*x*y = 0 in MATLAB and MATLAB still can't solve.
So I tried the cases of different integer values of a in MATLAB and the results are surprising:
It seems that MATLAB can solve the cases of odd integers $a$ but can't solve the cases of even integers $a$, except for $a=2$, which is accidentally solved by reduction of order.
Why MATLAB can solve the case of $a=2$ by reduction of order but not the cases of other even integers $a$? Can reduction of order in fact applicable for the cases of other even integers $a$? The usage of reduction of order has some limitations?