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Differential EquationsHardNumerical Methods: Euler to Runge–Kutta

Numerical Methods: Euler to Runge–Kutta · Hard problem

Apply one step of the classical fourth-order Runge–Kutta method with h=12h = \dfrac{1}{2} to y′=t+yy' = t + y, y(0)=1y(0) = 1, to estimate y(12)y\left(\dfrac{1}{2}\right). Express your answer as a common fraction.