For Equation 7.37, solve for the constants (A_{r}) and (B_{r}) by satisfying the initial conditions. M8 M8

For Equation 7.37, solve for the constants \(A_{r}\) and \(B_{r}\) by satisfying the initial conditions.

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M8 M8 u(x,t) = C, sin 3x(A, sin wrt + B+ cos wrt) 2 (2-1) sin -x mL 2L XA, sin (2-1) EA 2L m (2r 1) EA +B, cos t (7.37) 2L