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Differential EquationsEasyNumerical Methods: Euler to Runge–Kutta

Numerical Methods: Euler to Runge–Kutta · Easy problem

The backward (implicit) Euler method uses the slope at the new point: y1=y0+h f(t1,y1)y_1 = y_0 + h\, f(t_1, y_1). Apply one step with h=13h = \dfrac{1}{3} to y′=−3yy' = -3y, y(0)=1y(0) = 1. Express your answer as a common fraction.