Question

1) Find two power series solutions of the differential equation (x² + 1)y – xy + y = 0 about the ordinary point x = 0. Hint
Example 6 Power Series Solution Solve (x + 1), + xy - y = 0. Solution As we have already seen the given differential equatio
C-0 Ck+2 = 15%, k = 2, 3, 4,... Substituting de = 2, 3, 4,... into the last formula gives C = - = 0 + cyis nero 2s tosis ser
2 0
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(241) y ay ty zo put yz Žena neo ylz Coinox n21 guz E Cnon.onai).anan 722 putting these all in (241) ¿ Cn. n.67–13. 252 Ĉ Co... The series solution is +(+) 2 414 4 4*~4 (yx944, (x* * а со сч - - +94 *** *** --- - (-** 2-х + 24 25 - -- - ) + 2 со 24

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