how to solve second order differentials in matlab

To solve a second-order differential equation in MATLAB, we can use the ode45 function. This function solves the initial value problem for a system of first-order differential equations.

Here is an example code for solving the second-order differential equation:

main.m
% Define the differential equation
dydt = @(t, y) [y(2); -sin(y(1)) - y(2)];

% Set initial conditions
tspan = [0 10]; % Time span
y0 = [0; 0]; % Initial values of variables

% Solve the differential equation
[T, Y] = ode45(dydt, tspan, y0);

% Plot the results
plot(T, Y(:, 1))
xlabel('Time')
ylabel('y')
title('Solution of Second-Order Differential Equation')
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In the above code, we define the differential equation in the first line using an anonymous function dydt. The function takes two arguments, t and y, where t is the independent variable and y is a vector of dependent variables.

Next, we set the initial conditions for the differential equation by defining tspan as the time span over which the problem is to be solved, and y0 as the initial values of the variables.

Then, we solve the differential equation using the ode45 function, which takes the differential equation dydt, the time span tspan, and the initial conditions y0 as input arguments. The ode45 function then returns two arrays, T and Y, containing the time and solution values, respectively.

Finally, we plot the solution Y(:, 1) as a function of time T.