I was wondering if somebody would be able to help me with this problem. I know how to solve it using dimension arguments but I'm unsure what is meant by 'transform techniques'. Any help would be greatly appreciated.
An infinite horizontal plate moves with speed $U$ in its own plane relative to surrounding fluid. The plate is initially at rest relative to the fluid. The equations governed by $U_{t}(y,t)=\nu \nabla^2 U(y,t)$ with $U(0,t)=U$ and $U(y,0)=0$. Show using transform techniques that the boundary layers diffuse out from the plate with speed $\sqrt{\frac{\nu}{t}}$.