An isoperimetric constraint adds a constant to $y"$: the extremal is a parabola

The extremal of the isoperimetric problem $I(y(x))=\displaystyle\int_1^4(y')^2dx$ subject to the conditions $\displaystyle\int_1^4y\,dx=36$ and $y(1)=3$, $y(4)=24$ is: