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sol2 = ParametricNDSolve[{X'[t] == t + (Sqrt[3] / Pi) Log[a/(1 - a)] Abs[t X[t]] - X[t], X[0] == 1}, {X}, {t, 0, 2}, a]
(* ::Output:: *) (*
{x -> ParametricFunction[ <> ]}
*)

root2 = FindRoot[Evaluate[X[a][2] /. sol2] == 3, {a, .5}]
(* ::Output:: *) (*
[!] InterpolatingFunction: Input {2} lies outside the range of data... (InterpolatingFunction::dmval)
{s -> 1.40296}
*)

sol2 = ParametricNDSolve[{X'[t] == t + (Sqrt[3] / Pi) Log[a/(1 - a)] Abs[t X[t]] - X[t], X[0] == 1}, {X}, {t, 0, 2}, a]
(* ::Output:: *) (*
{x -> ParametricFunction[ <> ]}
*)

root2 = FindRoot[Evaluate[X[a][2] /. sol2] == 3, {a, .5}]
(* ::Output:: *) (*
[!] InterpolatingFunction: Input {2} lies outside the range of data... (InterpolatingFunction::dmval)
{a -> 0.812787}
*)

I suspect there is some internal bug with ParametricFunction that results in this behavior. How can I pin it down, and is there a current workaround? Is using ParametricNDSolve at this stage advisable at all?

How to understand this behavior, and is there a current workaround if it's a bug?

Related:

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