Find the extremals of ∫₀^{π/4} (y² − y′²) dx with y(0) = 0 and the right endpoint free on x = π/4

$Handwritten solution, page 1 of 1. Find the extremals of ∫₀^{π/4} (y² − y′²) dx with y(0) = 0 and the right endpoint free on x = π/4$