Use reduction of order to determine 2 linearly independent solutions of

(1 - x^2)y'' + 6xy' - 6y = 0

I realised that one of the solutions is x, so used the reduction formula to obtain a second solution of 1/5x^6 - x^4 + 3x^2 + 1... is this right? I've tried putting it back into the DE which gave 0 but I'm not not sure if that means its definitely right...

Thanks in advance!