10.1 Consider the following first-order ODE: dy dx = x/y from x = 0 to x...

 

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10.1 Consider the following first-order ODE: dy dx = x/y from x = 0 to x = 2.1 with y(0) = 2 (a) Solve with Euler's explicit method using h = 0.7. (b) Solve with the modified Euler method using h = 0.7. (c) Solve with the classical fourth-order Runge-Kutta method using h = 0.7. 2x The analytical solution of the ODE is y = +4. In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined. 3 10.1 Consider the following first-order ODE: dy dx = x/y from x = 0 to x = 2.1 with y(0) = 2 (a) Solve with Euler's explicit method using h = 0.7. (b) Solve with the modified Euler method using h = 0.7. (c) Solve with the classical fourth-order Runge-Kutta method using h = 0.7. 2x The analytical solution of the ODE is y = +4. In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined. 3