I have the following question that i am really stuck on please help.

consider the differential equation (1+x^2)y''-6y=0.

show that x=0 is an ordinary point of this equation - which i have done.

determine the interval in x for which the equation has a convergent solution of the form y=sigma(akx^k).

Show that the recurrence relation is

ak+2=-[(k-3)/(k+1)]*ak

and hence, determine the first six non-zero terms of the series solution.

please help.