# Autonomous system

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1. Nov 2, 2012

### thecoop

Hi guys

I have 5 term which each term includes three function of time (autonomous system ), i want to obtain time derivative of each term as other terms for example if i define each term as a dimensionless variable , e.g. x , y , z , v , w , i want to know dx/dt = as a combination of x , y , z , v , w.

In maple or mathematica or matlab is there any way to do it ?

thx

2. Nov 2, 2012

### Pythagorean

in matlab it requires the symbolic toolbox (which you have to pay extra for). I'm pretty sure mathematica comes automatically with symbolic math functions. No idea about maple.

3. Nov 2, 2012

### Pythagorean

try typing this:

(d/dt)t^2

into here:

http://www.wolframalpha.com/

for a taste of mathematica

4. Nov 2, 2012

### NemoReally

Mathcad also has symbolic differentiation and can do numeric differentiation if that would be better suited to your purpose.
Can you give an example of a couple of your terms?

5. Nov 2, 2012

### thecoop

1=ρ/3 H^2+x1+x2+x3+x4+x5

x1=ρ λ f/6 H^2
x2=-ρ λ f' R/6 H^2
x3=λ f" ρ R/H
x4=3 λ f' ρ
x5=ρ^2 λ f' / 3 H^2

where H=a(t) /a(t)

R=6(2H^2+H)

f(R)

ρ(t)

λ Constant
f' = the first derivative wrt R
f"= the second derivative wrt R
R=the first derivative wrt t
a`=the first derivative wrt t

I want each term derivation wrt to time expressed as other terms(x1 , x2 , ...) or at least have a Coefficient as R and f ( with its derivations wrt to R ) .

6. Nov 2, 2012

### thecoop

i don't know with what command i can do this !