## A tough problem for the weekend…

The contributor of this problem described it as “a (hard) problem to post up, if you want to scare students away”. Well, I think you’re made of sterner stuff than that — let’s see who’s right!

Find the function $y(x)$ that minimises the integral

$I= \displaystyle\int_{-1}^1 (x^4-y^6)^2(y')^{28} +\epsilon (y')^2 \mathrm{d}x$,

where $\epsilon>0$ and $y(-1)=-1$, $y(1)=1$.

It should at least keep you happily occupied if we have another wet weekend! Solutions to DP or MG in the usual manner…

(DP/NJM)