## Need help solving second order differential equations using ODE45

on 23 Feb 2012

### Jiro Doke (view profile)

Hey all,

This is my first post on the community so not entirely sure how it works but here goes!

I'm trying to solve a second order differential equation in the form:

```x'' = - (γ*x')+ (x*w^2)-(e*x^3) + F(t); where x is being differentiated with respect to t.
```

I've been asked to solve it using the ode45 function and I've spent a while looking at the help in MatLab but I'm stuck. I think I understand how the ode45 function works but I'm not sure how to put the differential equation into a form that Matlab will understand.

So far I have:

`   function dx = fx(t,x);`
```     %have global variables w, y, e, F
dx = zeros (2,1);
dx(1) = x(2);
dx(2)= -y*x(2) + x(1)*w^2 + e*(x(1))^3 + F;```
`   end`

and then I try:

`      [T,X] = ode45(@fx, [0 4000], [0 0 1]);`

I'm trying to integrate it over t=0 to 4000, and with the intial conditions x=0; dx/dt= 1; at t=0. I've looked at other examples but they've generally been just first order differentials with only two initial conditions. Do I have to add a 3rd part to my 'fx' function to take into account the dx/dt part of the equation, and how would I do this? I'm very much a MATLAB novice and any advice would be appreciated!

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### Jiro Doke (view profile)

on 23 Feb 2012

The initial conditions imply that t=0, so you simply need to pass in the two initial conditions for x and dx/dt. So for your example, [0 1], not [0 0 1].

Mark Purdy

### Mark Purdy (view profile)

on 10 Mar 2012

Hey, this was very useful, and put me on the right track, much appreciated!

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