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Student Support Forum: 'system of ODE's in matrix form?' topicStudent Support Forum > General > "system of ODE's in matrix form?"

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Mike Antonakakis
07/16/09 10:45pm

I'm doing some homework where I am trying to solve for two variables. I have an equation written in matrix form (if my math grammar isn't correct, I apologize). I have a few matrices:

q={{vy[t]},{r[t]} <-- these are the two variable I need to end up plotting vs time

q'={{vy'},{r'}}

A={{a,b},{c,d}}

u={{e},{f}}

where a,b,c,d,e,f are constants.

Now the equation given is q'=A.q+u. This gives me two differential equations:

vy'=a*vy+b*r+e

and

r'=c*vy+d*r+f

I don't have any issue using NDSolve to solve those two equations, I type this:

q = NDSolve [{vy'[t] == a*vy[t] + b*r[t] + e*dt,
r'[t] == c*vy[t] + d*r[t] + f*dt, r[0] == 0, vy[0] == 0}, {vy,
r}, {t, 3}]

and I get what I'm looking for.

So my question is, is there any way to skip the part where I find the two differential equations myself? In other words, is there a way I can input the equation in matrix form and solve for vy[t] and r[t] in one step?

I just started using Mathematica a few days ago, and have never used anything more complicated than a TI-83+ before this, so please excuse my lack of knowledge.

I've attached the file that works for me when I input the two equations myself.

Attachment: ch10-12hopefullyfinal.nb, URL: ,

Subject (listing for 'system of ODE's in matrix form?')
Author Date Posted
system of ODE's in matrix form? Mike Antonak... 07/16/09 10:45pm
Re: system of ODE's in matrix form? yehuda ben-s... 07/21/09 01:38am
Re: Re: system of ODE's in matrix form? Mike Antonak... 07/25/09 08:16am
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