MATLAB In Matlab, you can use ode45 to determine the solution y: [x_0, x_f] -> R for the ordinary differential equation

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MATLAB
In Matlab, you can use ode45 to determine the
solution y: [x_0, x_f] -> R for the ordinary differential
equation (ODE)
y' = dy/dx = f(x, y) and y(x_0) = y_0
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where
- x is the independent real variable;
- y is the dependent real variable, i.e., a function of x;
- [x_0, x_f] is the ODE solution function's domain;
- y_0 is the initial condition, i.e., the value of y at x =
x_0.
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The ODE with the initial condition is also called an initial
value problem.
To compute the solution y(x), ode45 takes as
first parameter a Matlab function that computes the values of f(x,
y).
A function can passed as a parameter either as
1. A string containing the function, e.g., "cos", "sin",
"my_function"
2. As a function handle using the "@" symbol, e.g.,
@cos, @sin, @my_function
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Consider the following ordinary differential equation (ODE)
dy/dt = f(t, y) = -y +2t
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Write a matlab script that
- contains a function which computes f(t, y); put the function
at the end of the script
- calls Matlab's ode45 function to compute the
values of y(t) for t between t_0 = 1 and t_f = 5 in increments of
0.2 and with initial value y(t_0) = 10; pass your function as a
function handle to ode45;
- stores the results for t and y(t) in variables
t and y, respectively.