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