## solving a second order linear differential equation

Asked by Eliraz Nahum

### Eliraz Nahum (view profile)

on 23 Sep 2018
Latest activity Answered by Eliraz Nahum

### Eliraz Nahum (view profile)

on 23 Sep 2018
Accepted Answer by Mischa Kim

### Mischa Kim (view profile)

hello everybody, I was trying to solve a simple pendulum second order linear differential equation of the form y''=-(g/l)*sin(y) while using the ode45 function. since it's a second order equation I understood that I have to manipulate the problem, so it will fit the ode45.
The mathematical manipulation I did is described in the attached picture.
g=9.8;
l=0.5;
t_span=[0 30];
F=@(t,q) [q(2);-(g/l)*sin(q(2))];
[t,q]=ode45(@(t,q) F(t,q),t_span,teta0)

R2018a

### Mischa Kim (view profile)

Answer by Mischa Kim

### Mischa Kim (view profile)

on 23 Sep 2018
Edited by Mischa Kim

### Mischa Kim (view profile)

on 23 Sep 2018

Almost there:
g = 9.8;
l = 0.5;
t_span = [0 30];
F = @(t,q) [q(2);-(g/l)*sin(q(1))]; % check your derivation
[t,q_t] = ode45(@(t,q) F(t,q),t_span,[teta0; tetad0])
This is a second order DE so you need two initial conditions, one for teta and one for tetad.

### Eliraz Nahum (view profile)

Answer by Eliraz Nahum

### Eliraz Nahum (view profile)

on 23 Sep 2018

thank you very much... sometimes it's not about the code, but the mathematics :-)