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Solve the following equation with RSolve and non-autonomous series?

F. P.
Posted 7 years ago

In this example, RSolve is not giving the result I'd expect (the parenthesis!). Am I missing something?

In[452]:= 
RSolve[{p[t + 1] == ( x[t] p[t] ) / ( 1 + b p[t] ), p[0] == p0}, p[t], 
  t] /. t -> 1

Out[452]= {{p[1] -> p0 / ( 1 + ( b p0 ) / x[0] )}}

I am using Mathematica 11.3 on Linux.
POSTED BY: F. P.
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F. P.
F. P.
Posted 7 years ago

Thanks Gianluca, that's what I mean. From the recursion 

p[t+1] = ( x[t] p[t] ) / ( 1 + b p[t] )
p[0] = p0

I expect

p[1] = ( x[0] p0 ) / ( 1 + b p0 )

but using RSolve I find

p[1] = ( x[0] p0 ) / ( x[0] + b p0 )
POSTED BY: F. P.

I would expect the result to be like this:

p1[0] = p0;
p1[t_] := (x[t - 1] p1[t - 1])/(1 + b p1[t - 1]);
POSTED BY: Gianluca Gorni

It is difficult to respond in the absence of a clear indication as to what was the expected result.
POSTED BY: Daniel Lichtblau
POSTED BY: Gianluca Gorni

Hi

You have 2 variables p[t] and x[t] then you need a 2 equations to solve.

Regards,MI
POSTED BY: Mariusz Iwaniuk
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