Calculus of variations — an extremal of a logarithmic functional

Suppose $y(x)$ is the extremal of the variational problem

$$J(y)=\int_0^4\frac{(y')^2}{y^2}\,\mathrm{d}x\quad\text{subject to } y(0)=1, y(4)=e^{8}.$$

Then which of the following statements is true?