Using the Weierstass condition, find the strongly minimizing curve and the value of for the cases

where .

I've gotten to a point where I have tried to continue, but I can't seem to get anything that resembles a correct solution.

Let

Using the Euler-Largrange eqn, I get

so ...(1)

which is a Euler's type DE which can be solved by changing variable .

Let . By the chain rule and noting that :

........(2)

and

....(3)

Subtracting (2) and (3) I get,

implying

which is equivalent to equation (1).

The extremal is therefore

Now, when using I don't get a solution that appears to be correct.....and I don't know how to continue. Any help would be greatly appreciated.

Thank-you.