the temperature in a 1 d bar is described by the diffusion equation fr

Question

The temperature in a 1-D bar is described by the diffusion equation, \frac{\partial u}{\partial t}=\alpha^{2} \frac{\partial^{2} u}{\partial x^{2}} Where a = (10+YZ) and YZ is the last two digits of your URN. If your URN is 6835725 then YZ =25. The problem has the following boundary and initial conditions: B C s:\left\{\begin{array}{l}
u(0, t)=0 \\
y(1, t)=0
\end{array}\right. I C: u(x, 0)=2 \sin (3 \pi x)-5 \sin (6 \pi x) Is the trial solution u(x, t) = g(t)sin(nn x) sensible for this problem, discuss why/why not. Using the trial solution u(x, t) = g(t) sin(nn x), convert the diffusion equation into a single ODE and find its general solution. Write the general solution to the PDE and solve for the unknown constants.