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Differential EquationsEasyNumerical Methods: Euler to Runge–Kutta

Numerical Methods: Euler to Runge–Kutta · Easy problem

The midpoint method takes the step y1=y0+h f ⁣(t0+h2, y0+h2f(t0,y0))y_1 = y_0 + h\, f\!\left(t_0 + \dfrac{h}{2},\ y_0 + \dfrac{h}{2} f(t_0, y_0)\right). Apply one step with h=12h = \dfrac{1}{2} to y′=yy' = y, y(0)=2y(0) = 2. Express your answer as a common fraction.