The minimum is . The condition gives one equation involving and , and the transversality condition gives another.
I need some help with the transversality condition.
I have a functional to minimize over an admissible class with one free end value
here it is
$int x'(1 + t^2*x')dt$
with $x(1)= 1$
the Euler equation gives me
$(1-c)/(2t) + c_1$
the transversality condition to be satisfied at $t= 2$ is
$f_x' (2, x(2), x'(2)) = 0$
can you please show me the steps to get c and $c_1$ using the transversality and the fixed end value?
thanks for the help