Extremal of a quadratic functional with fixed end values

Let $y(x)$ be the extremal of the functional

$$J[y]=\int_0^{\pi/4}\big((y')^2-4y^2+2xy\big)\,dx$$

subject to $y(0)=0$, $y\!\left(\tfrac\pi4\right)=1$. Then $y(x)$ is equal to