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Differential EquationsEasyNumerical Methods: Euler to Runge–Kutta

Numerical Methods: Euler to Runge–Kutta · Easy problem

The problem y′=2ty' = 2t, y(0)=0y(0) = 0 has exact solution y=t2y = t^2. One Euler step with h=15h = \dfrac{1}{5} is taken from t=0t = 0. Find the local error, the exact value y(15)y\left(\dfrac{1}{5}\right) minus the Euler estimate. Express your answer as a common fraction.