onsider the wave equation 52:1 621. air1 =15 E' -cxsz, nut} and we solve the equation by assuming separation oi variables of the form u[:,r] =F(.r}-...

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I.'.'.‘.onsider the wave equation 52:1 621.: air—1 =15 E' fl-cxszfi, nut}and we solve the equation by assuming separation oi variables of the form u[:r:,r] =F(.r}- (3(1), forD-Exsfi, :30.It is easy.F to see that new) 2 D for allx. I is a solution to this partial differential equation. and we areinterested in non-trivial solution. Suppose thatu(fl,r}= [land unit] =t} torallrzfl. Non-trial solution takes the form Hit 2 (En cosfln I] + Ca olefin I” 5i.o(% sax) . Enter the expression of in in terms of H and a“ in the box below using Maple syntax. irr=J JEE' Hence the solution takes the formIII u(1,;t) = 2 (Br: ccsfim I) + CH slurs-inn I” 5in(% our) .r1=1 The initial conditions areentail} = fisinfitx) +% sinflxx} andflu i} i}a {a J — .Calculate the exact values otfi'n and Cr: as requested below and enter them in the boxes. 3:5 = J Number J . CE. = J Number 312 = J Number J . {312 = J Number J .