Consider the following condition and solve the one dimensional wave equation using Dalembert's Method.

$\frac{de{l}^{2}y}{del{t}^2}=25\frac{de{l}^{2}u}{del{x}^2}$

$u(x,0)=x^2$

$u_t(x,0)=5cos5x$

Solve the unsteady state, one dimensional heat conduction equation $)=(2u_{}$ considering the following conditions;

$u(0,t)=0$

$u(2,t)=0$

$u(x,0)=5sin4x$

Use Separation of Variables method.