Question

Without looking for the solutions in a power series around Xo given, determine the radius of convergence for such solutions in series for the differential equation:

(x^2 + x-12)y"+(x^2-1)y'+3y=0
and the values for Xo= -5, 0, 6

Answer 1

The solution will exist in all intervals where the functions dont vanish

We note that these functions are zero if and only if:

and

Thus, the solution is convergent in all intervals except those containing

The largest such interval containing is which has a radius of convergence

The largest such interval containing is which has a radius of convergence

The largest such interval containing is which has a radius of convergence

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