Needed to be solved correclty in 20 minutes please solve correctly and provide correct option 0, whichsatisfies the boundary conditions u(0, t) = u(3, t) = 0 and the initialconditions u(x, 0)Ut(x,...

Needed to be solved correclty in 20 minutes please solve correctly and provide correct option

Extracted text: The solution of the wave equation Urx Gutt. 0 < x="">< 3.="" t=""> 0, which satisfies the boundary conditions u(0, t) = u(3, t) = 0 and the initial conditions u(x, 0) Ut(x, 0) = 2 sin() - 3 sin(2rx) + 2 sin(3rz) is O and -- 2nnt. u(x, t) = E sin () [an cos (2at) + b, sin COS 3 where 3 n=1 O a) b1 = 2, b6 -3, bg = 2, bn O otherwise an O b) b1 = , , be = 7, bg ==, b, = an = 0 otherwise C a1 an = bn O otherwise a6 47 ag -3, ag 2, an 0 otherwise d) ai 2, a6 O e) None of these