Question $4(7pts)$: We will soon need to solve the following ODE:

$\frac{d^{2}Y}{d{x}^2}=B^{2}Y$

where Y is dimensionless, whereas $x$ has units of length, and therefore $B$ must have units of

reciprocal length. The boundary conditions are $Y=1$ at $x=0$ and $\frac{dY}{dx}=0$ at $x=L$

a$.$ Refer back to your DiffEq class to remember the general solution to this ODE. Then substitute

the boundary conditions to get the particular solution.

b$.$ Take $B=27\mathrm{.}6m^{-1}$ and on a single graph, plot $Y(x)$ for $L=10mm,L=30mm,$ and $L=100$

mm $.$ Save your work since we will need it later.