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Differential EquationsEasyNumerical Methods: Euler to Runge–Kutta

Numerical Methods: Euler to Runge–Kutta · Easy problem

In one classical Runge–Kutta (RK4) step for y′=t2+yy' = t^2 + y from the point (t0,y0)=(1,2)(t_0, y_0) = (1, 2) with h=0.2h = 0.2, the first two stages are k1=f(t0,y0)k_1 = f(t_0, y_0) and k2=f ⁣(t0+h2, y0+h2k1)k_2 = f\!\left(t_0 + \dfrac{h}{2},\ y_0 + \dfrac{h}{2} k_1\right). Find k2k_2. Express your answer as a decimal.