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Having exams on monday but still having problems with PDE. I thought i got it until i saw the teacher's solution different from mine and i have no idea wtf she doing also.. Contacting her is not an option. Please give me a hand with this.. Much appreciated.

Solve the equation of vibrations of a stretched string of length 2,

d2u/dt2 = 16 * d2u/dx2 (0<x<2)

*2nd order differential

for t>0. The string is clamped at each end, so that the boundary conditions are:

u(0,t) = u(2,t) = 0

At t=0, the initial displacement of the string is,

u(x,0) = 2sin (pi * x)

and its velocity

ut(x,0) = 2sin (pi/2 * x)

*t is a subscript

2. Relevant equations

3. The attempt at a solution

Below is my attempt,

This is the lecturer's solution,

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# PDE wave equation.

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