Don't think so, but I'm not sure how the problem is actually stated.
Is it
a)[tex]y = km~ln(\sqrt{cosh(gt/(km))}~)[/tex]
or
b)[tex]y = km~ln(cosh(\sqrt{gt/(km)}~))[/tex]
?
As you wrote the problem, it would be a, but your derivative (which should be dy/dt) suggests it is b.