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)
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,
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