Question

Use a power series centered about the ordinary point x0 = 0 to solve the differential equation (x − 4)y′′ − y′ + 12xy =...

Use a power series centered about the ordinary point x0 = 0 to solve the differential equation

(x − 4)y′′ − y′ + 12xy = 0
Find the recurrence relation and at least the first four nonzero terms of each of the two linearly inde-

pendent solutions (unless the series terminates sooner).

What is the guaranteed radius of convergence?

0 0
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Answer #1

(x-47 o let Σa, n-d nant eu n-2 Pautiring get the clifferenticl equatin, we -2 2 na)an - 4 n(n-) Cun nti (a n d -1 ,Cay 7(nt2n4200) ani- 4 (nt2) (nti) ant2 n Kt12an t 12 an 4.2.02 Compuriny bath aids,we get - ga2-a= 0 (ntin anri -4 (nt)(nt) antz an+iSo the Series Bolution girer a 3 y - 2 +a +02 3 4 3 ao 32 aotc4n 4 4 1 4 3 2

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