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Re: (in)dependent variables in DSolve: need explanation.

• To: mathgroup at smc.vnet.net
• Subject: [mg73500] Re: (in)dependent variables in DSolve: need explanation.
• From: P_ter <peter_van_summeren at yahoo.co.uk>
• Date: Tue, 20 Feb 2007 06:20:03 -0500 (EST)

Hello,
Thanks for putting my question again.
When I look back at my ealier text, well maybe it is not all to clear. 
I have this z dP(z,t)/dt = (1-z)((a - b z)* P(z,t) - bP0(t))  with P(z,0)=z^i (i given).
I would like to solve this equation by means of the Laplace transform.

.......................(z^(i+1) - b (1-z)Laplace(P0(t))
 Laplace[P[z,t]] =     ---------------------------------
............................(sz - (1-z)(b - az)

To have a solution one must find the roots of (sz - (1-z)(b - az). For the suitable root the denumerator has to vanish, otherwise the Laplace[P[z,t]] would not exist.
This gives Laplace(P0(t)). Substitute it in Laplace[P[z,t]]  and one has to find the inverse. That is by hand quite a problem.
I was just wondering if someone had done this already.  
with friendly greetings,
P_ter