Consider the differential equation (x 2 + 1)y ′′ − 4xy′ + 6y = 0. (a)...

Consider the differential equation
(x
2 + 1)y
′′ − 4xy′ + 6y = 0.
(a) Determine all singular points and find a minimum value for the radius 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 all necessary 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.

Expert Solution

Colby Messinger answered 1 year ago

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