Numerical Methods: Euler to Runge–Kutta · Hard problem

Euler's method with $h = \dfrac{1}{2}$ is applied to the oscillator system $x' = y$, $y' = -x$, starting from $x(0) = 1$, $y(0) = 0$. After two steps the point is $(x_2, y_2)$. Find $x_2^2 + y_2^2$. Express your answer as a common fraction.