Hello everyone!

Now this is a pickle...

2xy''-(1+2x^2)y'-xy=0.

It is required to determine the indicial roots of this DE.
(a) 1, 3/2.
(b) 0, 3/2.
(c) -1, 2/3.
(d) 0, -3/2.
(e) \text{None of the above.} \\


After unifying the powers of the xs we get 2 pairs of sums, one pair starts with the index of k=-2 and the other with k=0.

So if we intend on not replacing any value for k, we gets r=\frac{1-2k}{2} \text{and} r=-1-k. But when we replace k for -1 or -2 we get 2 different sets of values!!

What to do?!