Numerical Methods: Euler to Runge–Kutta · Challenge problem

The backward Euler step for $y' = y^2$ from $y(0) = 1$ requires solving $y_1 = 1 + h\,y_1^2$ for $y_1$. What is the largest step size $h > 0$ for which this equation has a real solution $y_1$? Express your answer as a common fraction.