4. Solve the initial value problem utt = 9uxx, u(x, 0) = 9uxx, u(x, 0) = 1+x², ut(x, 0) = 0 and interpret the solution in the context of waves.
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- Find the solution of the wave equation when initial velocity equal to 0 and initial deflection is (2kx/l) when x between zero and (1/2) and deflection equal to (2k(l-x)/I) when x between (1/2) and (I) the P.D.E. is * c2 dx²2. The position vector of a particle is given by r(t)= (2 cos t sin t)i +(cos^2 t - sin^2 t)j + (3t)k If the particle begins its motion at t = 0 and ends at t = pi, find the difference between the length of the path traveled and the distance between start position and end position+0o Find Ul-1/i, 1/i]. i=1