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Question: Neutral DDEs with 'consistent' initial conditions?

Question:Neutral DDEs with 'consistent' initial conditions?

sursumCorda 1324 Maple 2023
dsolve numeric differential-equations dde
July 14 2023
1

I'd like to reproduce Initial Value DDE of Neutral Type in Maple.
The differential equation is: 

deq := D(y)(t) = 2*cos(2*t)*y(t/2)^(2*cos(t)) + ln(D(y)(t/2)) - ln(2*cos(t)) - sin(t): # with y(0) = 1 and known D(y)(0)

Unfortunately, if I type valid initial values, Maple will simply generate Error, (in dsolve/numeric/DAE/initial) too many initial conditions, the following are not needed: {D(y)(0) = 2}, and yet if I just give a partial initial condition, Maple will display Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up and only return incorrect results. 
 

> 

restart;
> 

interface(version)

`Standard Worksheet Interface, Maple 2023.1, Windows 10, July 7 2023 Build ID 1723669`

 (1)
> 

deq := (D(y))(t) = 2*cos(2*t)*y((1/2)*t)^(2*cos(t))+ln((D(y))((1/2)*t))-ln(2*cos(t))-sin(t)
> 

RealDomain:-solve(subs(t = 0, y(0) = 1, deq), (D(y))(0))

2, -LambertW(-2*exp(-2))

 (2)
> 

dsolve({deq, y(0) = 1, (D(y))(0) = (2, -LambertW(-2*exp(-2)))[1]}, 'numeric', 'delaymax' = Pi, 'range' = 0 .. 2*Pi)

Error, (in dsolve/numeric/DAE/initial) too many initial conditions, the following are not needed: {D(y)(0) = 2}

  
> 

dsolve({deq, y(0) = 1, (D(y))(0) = (2, -LambertW(-2*exp(-2)))[2]}, 'numeric', 'delaymax' = Pi, 'range' = 0 .. 2*Pi)

Error, (in dsolve/numeric/DAE/initial) too many initial conditions, the following are not needed: {D(y)(0) = -LambertW(-2*exp(-2))}

  
> 

dsn := dsolve({deq, y(0) = 1}, 'type' = 'numeric', 'delaymax' = Pi, 'range' = 0 .. 2*Pi)
> 

plots['odeplot'](dsn, 0 .. 2*Pi)NULL

Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

  

`[Length of output exceeds limit of 1000000]`

  

Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

  

 


 

Download ndelay.mw

The output is wrong. Note that "y(0) = 1" is insufficient to uniquely specify a solution, as "D(y)(0)" can be either -LambertW(-2/exp(2)) or 2. But Maple does not allow sufficient constraints here. How do I avoid such an unexpected behavior?
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