Question

. (a) Find the general solution to the following differential equations. Express your answer in terms of Bessel functions of the first and second kinds (just as we did in assignments, do not write the asnwers as series expansions of Bessels functions). Please explain how you arrived at your answer. (b) Please start with separation of variables and completely solve the heat flow problem. 2 Ll ot u(0, t) u(2, t)=0 = -(ま 1, 0<<1

Answer 1

Solution:

utfon.- 3 a Gfven -that 七4 s ztiontuîns to Bessel after Qimple change of Variab le n, dメ at dy dt dl. 3 db

so, substi tute 、the above vat as 3 ,we get ' 七 七 3 This ts a Besse l eg uation for ут 7

Giventhau ると eyau 2.

(nm) je> 을.cn sin í..®..) where Cn- LA MTT

tHenee d 6