2nd Order ODE by ode45

Hi community, i request assistance in getting the code for this particular question.

I tried watching yotube and looking around matlab answer but i still don't understand the approach in solving it.

Please advice, thanks.

Answer 1

[Per Hyldahl]

Hi,

You need to treat your 2nd order differential equation as a system of two 1st order equations and arrange them in a vector, like:

f = [y; y']

such that

f' = [y'; y'']

Then you can obtain the solution using the following code

clc; clear; close all

[t,y] = ode45(@deriv, [0, 25], [0, 0]);

plot(t, y(:,1), t, y(:,2))
legend('y(t)', 'y''(t)')


function f_prime = deriv(t,f)
    f_prime = zeros(2,1);
    
    f_prime(1) = f(2);
    f_prime(2) = 3*cos(t) -1.5*sin(t) - 3*f(2) - 3.25*f(1);
end

I myself also had problems to wrap my head around this approach when i learned it :)

// Per

[David Lee]

I know [0,0] is from the initial condition

But may I know how you derived the number [0, 25]

[Per Hyldahl]

The array [0, 25] is the time vector and I just chose som arbitrary number; hence starting at t= 0s and endning at t=25s

[David Lee]

Then how does the function at the 2nd part of the script contribute to the plot when its made after the plot of the graph?

[Per Hyldahl]

Hi,

The sub-routine 'deriv' is a function which evaluates the differential equation, and is given to the ode45 as an input argument.

As Hiro-San suggested in a different answer, you should read the documentation of the ODE-solver suite; e.g. for ODE45: https://www.mathworks.com/help/matlab/ref/ode45.html.

Especially, the section regarding input arguments.

/ Per

[David Lee]

Thanks!

Answer 2

[Hiro Yoshino]

You can walk through this:

https://www.mathworks.com/help/matlab/ref/ode45.html

I guess this is what you work on - read, understand and apply to your homework.