# 2nd Order ODE by ode45

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David Lee on 19 Feb 2020
Commented: David Lee on 22 Feb 2020
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.

Per Hyldahl on 19 Feb 2020
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 on 19 Feb 2020
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 on 20 Feb 2020
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 on 22 Feb 2020
Thanks!