Question: Can you please solve the below question (Task 1)? Task 1: Numerical Solution of Differential Equations Solve the equations, dy dx dy dx = 2

Can you please solve the below question (Task 1)?

Task 1: Numerical Solution of Differential Equations Solve the equations, dy dx

Task 1: Numerical Solution of Differential Equations Solve the equations, dy dx dy dx = 2 sin(x) + y, y(0) = 1 = x + 3x + 2-2y, y(0) = -1 using Euler's, Heun's and Runge-Kutta methods. Compare your results with the analytical solutions. If necessary, solutions using built-in MATLAB functions, could be substituted in place of either the analytical (i.e. as the reference) or Runge-Kutta solutions. They should be well-justified in terms of the particular function employed and any settings used to control it. (14 Marks) Use your comparison to show how the step size used within the algorithm affects the accuracy of the solution. (6 Marks)

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