$$ u_{tt} $$=$$ u_{\times\times} $$ with u(x, 0)=x and $$ u_{t}\left(x,0\right)=0\text{  }u\left(0,t\right)=t^2 $$  u(1,t)=cost

To solve the given partial differential equation with specified boundary and initial conditions, we'll follow the method of separation of variables.

The given PDE is:
\[ u_{tt}

Learn how to solve the partial differential equation u_tt = u_xx with given initial and boundary conditions. This problem involves applying the method of separation of variables to find a solution. Suitable for advanced undergraduate students and researchers.

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