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Differential EquationsMediumNumerical Methods: Euler to Runge–Kutta

Numerical Methods: Euler to Runge–Kutta · Medium problem

Apply Euler's method with step h=12h = \frac{1}{2} to y′=y+xy' = y + x, y(0)=3y(0) = 3. Find the approximation to y(1)y(1) after two steps. Express your answer as a common fraction if needed.