Math 257/316, Midterm 2, Section 10417 November 2008Instructions.The duration of the exam is 55 minutes. Answer all questions. Calculators are not allowed.Maximum score 100.1. Solve the following inhomogeneous initial boundary value problem for the wave equation:utt=c2uxx+e−tsin (5x),0< x <π2, t >0u(0, t)=0andux(π2, t) =t,t >0u(x,0)=0,ut(x,0) = sin 3x+x,0< x <π2[60 marks]2. Use separation of variables to solve Laplace’s equation for the square plate:uxx
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