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vectorial ODE in mathematica

  • To: mathgroup at
  • Subject: [mg126768] vectorial ODE in mathematica
  • From: volatility quant <volatility.quant at>
  • Date: Wed, 6 Jun 2012 04:52:33 -0400 (EDT)
  • Delivered-to:

I want to solve the following equation in mathematica :

DSolve[{X'[t] == A.X[t], X[0] == ( {{0},{0}} )}, X[t], t]
It is a system of 2 ODEs coupled by the matrix A, that I don't want to
put in the form {{a,b},{c,d}} in order to have the output as a
function of matrix exponential.

Mathematica understands that but gives a solution strangely expresed
as :

 {{X[t] ->
     InverseFunction[Dot, 2, 2][A,
         E^(t A.1)
         InverseFunction[InverseFunction[Dot, 2, 2], 2, 2][A, 0]]}}
Where it indeed uses a matrix exponential, but also relies on a
strange notation InverseFunction [...]

My question is how to get rid of this InverseFunction notation to have
a more readable expression. Do I for example have a manner to
postulate that A is a (2,2) matrix, invertible, with inverse B?

Thanks a lot for help

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