G25 solution has a different ode then in paper ?

Download G25_heeft_andere_ode_dan_gegeven_mprimes_30-5-2025.mw

"Could there be a mistake in my assumptions, or are some of these solutions only valid under specific conditions?

Also depends on some mathematical function type what the solution is , according to me with the scaling I suspect?

@salim-barzani 
All those solutions for Z , have certain conditions to get them to 0 in an odetest.
What are they ?
Download geschaalde_riccatie_ode_mprimes_29-5-2025_A.mw

@nm 

q0 and q1 can be 0 , but not q2 =0 ( no riccatie ode anymore) 


   is a Riccati form 

The combination of the 3 functions in the Riccation ode makes many ode forms possible

General form : 

@vv 
I don't use Copilot,but perhaps idea 
That's promising that the ai's don't come up with divergent reasoning

Although Maple cannot directly arrive at a stepwise result of the final result: 5/2 , the reasoning leading to the final result is informative

@vv 
 "generated by AI, probably Microsoft Copilot".:.. no, you need more clever ai then copilot

I do have some study maples worksheet for handling infinty series 
Not expensive to buy the whole lessons series with  different topics from Harald Pleym author
For real numbers, not complex 
For complex series there is probably to find  something

FunctionAdvisor(Psi);

Psi
the Digamma and Polygamma functions

@Alfred_F 
I am not a expert in Special functions 

A special function
Then there exist a closed form as it seems.  

With the functionadvisor  in Maple you can get information about this digamma function ? 

@Alfred_F 


here you can the factor j in front of the infinite sum over k?, by multiplying with j  for left en right side of this equation

Also 


by induction 

restart;
assume(j::real);

# Definieer P(n) met optie 'parametric' voor de sommen
P := n -> j * sum(1/(k^2 + j^2), k = 1..n, parametric) - sum(j/(k^2 + j^2), k = 1..n, parametric);

# Basisgeval
P1 := simplify(P(1));  # Geeft P1 := 0

# Inductiestap
delta := simplify(P(n+1) - P(n));  # Geeft delta := 0
P := proc (n) options operator, arrow; j*(sum(1/(j^2+k^2), k = 

   1 .. n, parametric))-sum(j/(j^2+k^2), k = 1 .. n, 

   parametric) end proc

                            P1 := 0

                           delta := 0

@nm 
Now I am curious,what is the reason for giving the ode general solution now via a parameter solution?
Yes, linear ode are solved easier directly with known functions while this is not possible with non -linear odes

@nm 
"Not sure I understand the question. If you mean how to ask Maple for implicit solution to an ode, then the option 'implicit' is used for this."
Linear or non-linear odes:  is there difference for trying to get parameteric solution for both types of ode?

SimuleerSysteem(3, 2, 1, 0, -5, 1);
- y axis must be Re/ Im and other plot title 

The question now is how maple performs linear and non-linear odes with the implicit option for a solution ? 

flowdiagram using