Question

Without looking for the solutions in a power series around Xo given, determine the radius of...

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

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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

Please don't forget to rate positively if you found this response helpful. Feel free to comment on the answer if some part is not clear or you would like to be elaborated upon. Thanks and have a good day!

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