Question

10. Find all singular points of the following equation and determine whether each one is regular or irregular?* (8 Puan) (1 - 1)?y" + 2xy' + 4y = 0

Answer 1

0 solution : Given that 22 (1-8973" +990'+ 4y = 0 corsideo Acodi +260 + 9,007o —O da o definition: i) If Pola) #0 Then 0-Q is called an codinary codinary point of otheawes a Bizgular poid if. when 0 Segulat ii) singulat point -Q of is called ispul in the room de a candy ada + 4 Olot) la-a) ig=0 2 a-a da wheoe 2, (01) and Bg lo) pooccisega deovalivals of all oodeos in the neighboudhood of a *h? A sigubo point which is not oogelet io cellos an Bodegular singeky, paint Given doo-oºry"+pay'+4y=0 - acralo only if 0:0Jand these Edcept 0:0, 1. The other seal numbers are an oodiangy point of a Bizgubipoints of a

1-ya a=0 is an point of @ Q ooegulat singulat ☺ din-033" + oy'tuyo (1-02) at yoo wheoc 2,100) - qa 011-02) all oodoos in doco not poogscos decialives of neighbourhood of a=0 orgulat singular point of @ any a= 1 is a @ 3061-033"tawy'tky 0 1) Y"+ sacra} -Y": व२ (1-222 y=0 Y", rekao udi-a? + a raay" Ý 0 (1-a272 Wheoer 0,60) - uc1-02) 2 og (0) passes derivalco a of all codess in a neighbourhood of a-o. Thank you

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