Needed to be solve this multiple choice question correctly in 30 minutes and get the thumbs up please show neat and clean work please 0, whichsatisfies the boundary conditions u(0, t) = 5 and u(1,t)...

Needed to be solve this multiple choice question correctly in 30 minutes and get the thumbs up please show neat and clean work please

Extracted text: The solution of the heat equation Ura Ut. 0 < x="">< 1.t=""> 0, which satisfies the boundary conditions u(0, t) = 5 and u(1,t) = 1 and the initial condition u(x, 0) = x has the form u(x, t) = v(x) + E bn sin(nrx)e n²x²t, where n=1 O a) v(x) = 5 – 4x and bn 10 (a 1) sin(nr2) dr O b) None of these c) v(x) = 5 4x and bn = 2 a sin(nTr) dr O v(x) = 5 d). 4x and bn 10 S (1 – 2) sin(nA2) dr e) v(x) = x + 5 and bn 2 So z sin(nr2) de