$(35$ points$)$ Consider a fluid with variable viscosity near a plate that suddenly is set in motion with a constant velocity $U_0.$ The governing equation is given by

$\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{t}}=(y{t}^5)\frac{de{l}^{2}u}{del{y}^2}$ for $,y0$

The boundary conditions are:

$u(y,0)=0,u(0,t)=U_o,$ and $u(,t)=0$

a$)$ Find the appropriate similarity variable $,$ and reduce the governing equation and boundary conditions to the similarity form.

b$)$ Evaluate the solution.