Question

Detail greatly appreciated thankyou

Find the solution of the inhomogeneous heat equation Uxx = U/ +2,0 < x < 1,t> 0; u(0, t) = 0, u(1,t) = 0,t > 0, u(x,0) = x2 – x. Hint: Find a stationary solution first and then ..., then use the computation in Q3.

Answer 1

, Их = 4 + 2 оси , +70) »« – Чxx = 10)+ )=0 , щь,+)=0, + 7 — 0 Чех,) = х2-4. Па 14* - 40 и зим Т. или). хор, от te) се, і че) where on = {{qca, cincang hot + {- teyimlaxyx ) "fi,t)= -., l=1, +ts) =-х, к=) ,че, у ='es{ Pota ax - регунтуки , таке ~ [e-эј не з!--[-тен (*))) р, = Го - от 45а (cont-1) - - | by = = (-) ) - так сну 5,1%) = 1 Г-2 біттях4х = -40 smerx јая hte) --- (- *)" - («сиқ-si) Фte) - Artet-) ) - р

Now by eqn@, e dopusta? mt mtha (s-t) ucxit) - I Din sin (max) e sin falsas no M T n=1 Now using Eqr ② & ④ in above, UCH) = 8:1-1) sim kurse mit sin may "-), = 4 5y". ) dimenany z pirt Latat de as " 9242(S-t 924215-t) as it gets sl. ne- -nrit I n22 nel InnKX MBK3 껴

ητα) UlXit) = η33 Υ