Using matlab/mathematica to solve a second order diff.eq.

[astropi]

Homework Statement

This is NOT a homework problem, but it is similar. Anyway, let's say we have:

y''+3y' = 2t^4

This is easy to solve by hand. For the particular solution you get:

Yp = At+Bt^2+Ct^3+Dt^4+Et^5

Now, to solve for the coefficients, you can solve them by hand, or you can use some sort of program. Myself, I tried using MATLAB but could not get it to work. So I am hoping someone with MATLAB experience can help me, since I do not want to do all this mundane work by hand!

Homework Equations

You have to take the derivative (1st and second) of Yp and then plug back into the original equation, then equate coefficients. Although it can be done by hand, surely there has to be a better way to do this with Mathematica or matlab?

The Attempt at a Solution

I tried using matlab, as I said, but could not get it to work. If someone has an idea, or wants to see my MATLAB code (which is only 4-5 lines) I would be happy to send it. Otherwise, if someone can help with either MATLAB or mathematica, please let me know. Thanks.

 

[hunt_mat]

I think you have to treat it as a system:

$$\begin{array}{rcl} y' & = & z \\ z'+3z & = & 2t^{4} \end{array}$$

 

[astropi]

I think you have to treat it as a system:

$$\begin{array}{rcl} y' & = & z \\ z'+3z & = & 2t^{4} \end{array}$$

I don't follow you. How is this going to help me use Mathematica or Matlab? If you know how, please provide me with some actual code I could test out. Thanks.

 

[hunt_mat]

|If you look in the help files, it's quite clear how to use the ode45 routine to solve a system. Matlab won't solve higher order systems, you have to break them down into first order systems.

 

[astropi]

|If you look in the help files, it's quite clear how to use the ode45 routine to solve a system. Matlab won't solve higher order systems, you have to break them down into first order systems.

I'm a MATLAB newbie, so ode45 doesn't look very clear to me. Do you have to have initial conditions for ode45 to work, because in my example there are none. Also, I was fairly certain you can use dsolve to solve second order diff. eq. without much problem. At any rate, I'm not trying to solve the diff.eq. I already did that. I just want some program to do the algebra. Thanks.

 

[hunt_mat]

Then use maple or matlab.

 

[astropi]

Then use maple or matlab.

I have been trying matlab. I don't know maple, but I would be surprised if people haven't already done this with Mathematica and Matlab. Hopefully someone out there can help...