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…


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