# Differential equation for matlab

1. Oct 12, 2012

### cameuth

THE PROBLEM :

y(t) = e^(-t)*sin(t^2);
with t0 = 0 and T = 3.14159. Find y_0, and use it to deduce the corresponding expression
for f(t, y) (Your f should have both a t and a y in it. Simplify it to find the y!).

This is for a matlab project. I've solved this differential equation (which we get from the derivative of the problem above) , but apparently there's a way to solve it where we get y on the right hand side of the equation (and still have t's). This is the only way the code will work in matlab.

MY ATTEMPT: basically I took the derivative of y=e^(-t)*sin(t^2) to get

y'=-e^(-t)[sin(t^2)+(2t)cos(t^2)]

You then inegrate to get the original formula plus a constant

y=e^(-t)*sin(t^2)+C

Now if we apply the inital condition y(0)=0, we get the original equation. Again.

y=e^(-t)*sin(t^2)

This is not correct. What am I missing?

PS, if you want to see my code and think that will help I have that as well. Just ask. Thanks

Last edited: Oct 12, 2012
2. Oct 12, 2012

### Staff: Mentor

are you doing something with FFT (aka fourier transforms) on the equation?

Thats what people often use matlab for given a complicated signal and use FFT to determine the component frequencies.

Last edited: Oct 12, 2012
3. Oct 12, 2012

### cameuth

No, I'm trying to approximate this differential equation using the runge-kutta method, then plot the error. But, I can't really do any of that without the proper differential equation. Which is where I'm stuck.

4. Oct 12, 2012

### Staff: Mentor

Okay so given a differential equation, you want to use matlab to numerically integrate your equation via runge-kutta and to then compare it to an exact solution.

Have you tried a simpler equation such as integrating a sin function to get a cos function to test your matlab code?

To be fair, I'm not a heavy matlab person. I've done some numerical integration using open source physics java code where we converted the differential equation into first order differentials and I figure that's how it may need to be done here.

I did find this predator prey simulation that compares two versions of runge-kutta in plot form that may help.

http://math.arizona.edu/~emcevoy/odes.pdf

Last edited: Oct 12, 2012
5. Oct 14, 2012

### X89codered89X

When you wrote:

$y(t) = e^{-t}sin(t^2)$, did you find this, or was this given to you? I'm confused. Precisely what does the problem give you?

6. Oct 14, 2012

### X89codered89X

So, I'm still confused about what f(t,y) is supposed to be, but I got

$\dot{y} = e^{-t}(-sin(t^2)+2tcos(t^2)) = -y+2te^{-t}cos(t^2) = f(t,y)$

is this useful at all?