10.2 Consider the following first-order ODE: $\frac{dy}{dx} = x - \frac{xy}{2}$. from $x = 1$ to $x = 3.4$ with $y(1) = 1$ (a) Solve with Euler's explicit method using $h = 0.8$. (b) Solve with the modified Euler method using $h = 0.8$. (c) Solve with the classical fourth-order Runge-Kutta method using $h = 0.8$. The analytical solution of the ODE is $y = 2 - e^{\frac{1-x^2}{4}}$. In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined.
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We can do this by creating a function in MATLAB that takes in the current value of x and returns the value of dx/dt. Here's the MATLAB code for the function: ```matlab function dxdt = ode(a, x) dxdt = a; end ``` Now, let's solve the ODE using Euler's Show more…
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