Consider the differential equation
(x
2 + 1)y
?? ? 4xy? + 6y = 0.
(a) Determine all singular points and find a minimum value for theradius of convergence of
a power series solution about x0 = 0.
(b) Use a power series expansion y(x) = ??
n=0
anx
n
about the ordinary point x0 = 0, to find
a general solution to the above differential equation, showing allnecessary steps including the
following:
(i) recurrence relation;
(ii) determination of all coefficients in the power series;
(iii) final form of general solution as y(x) = c1y1 + c2y2.
