Re: Volterra Equation?
- To: mathgroup at smc.vnet.net
- Subject: [mg79480] Re: Volterra Equation?
- From: chuck009 <dmilioto at comcast.com>
- Date: Fri, 27 Jul 2007 06:02:39 -0400 (EDT)
I think you're missing an x for a Volterra equation right:
y[x]=Integrate[(1/y[t]+k),{t,0,x}]
otherwise it's a homogeneous Fredholm equation. Anyway, a Volterra equation like that, just differentiate both sides and then use DSolve:
DSolve[Derivative[1][y][t] ==
1/y[t] + k, y, t]
Out[85]=
{{y -> Function[{t},
(-1 - ProductLog[
-E^(-1 - k^2*(t +
C[1]))])/k]}}
> Hi:
>
> I was wondering this equation could be solved in
> Mathematica:
>
> B(x)=Integrate[1/(B(r)+k,r,0,a]
>
> Thanks,
> Angela Kou
>