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Re: Mathematica DSolve Terminal Boundary- How?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68239] Re: Mathematica DSolve Terminal Boundary- How?
  • From: Peter Pein <petsie at dordos.net>
  • Date: Sun, 30 Jul 2006 04:48:17 -0400 (EDT)
  • References: <eaer6i$59t$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Ajaz Hussain schrieb:
> Hi,
> 
> I am trying to find a general solution for a differential equation from t = o to t = T. I know that y[T]== 0 but don't know y[0]. How do I "fool" DSolve to give me a solution? The manual gives this command for boundary values:
> 
> DSolve[ {eqn == 0, y[o] == initial value}, y[x], x]
> 
> I want to instead have: y[T] = terminal value
> 
> Thanks!!
> 

Hello,

  it /is/ possible, to use boundary conditions.

  A simple example:

In[1]:= soln = DSolve[{y'[t] - y[t] == 1/Cosh[t], y[T] == 0}, y, t];
In[2]:= f = y /. First[soln]
Out[2]= Function[{t}, (-E^t)*(Log[1 + E^(-2*t)] - Log[1 + E^(-2*T)])]

In[3]:= f[T] == 0
Out[3]= True

In[4]:= f[0]
Out[4]= -Log[2] + Log[1 + E^(-2*T)]


Peter


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