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