Hello all,

I am trying to find an "easy way" of getting the possible values for a "a" parameter in the following differential equation:

solutions = ParametricNDSolveValue[{y''[t] - ArcTan[y[t]] + y'[t]^2 == a,  y[0] == y[1] == 0}, y, {t, 0, 1}, {a}]

It's easy to plot them as following, for instance:

Plot[Evaluate[Table[solutions[a][t], {a, -4, 5, .5}]], {t, 0, 1},  PlotRange -> {{0, 1.1}, {-0.6, 0.6}}]}

and also to manipulate and visualize the "a" parameter doing:

Manipulate[Plot[solutions[a][t], {t, 0, 1}, PlotRange -> {{0, 1}, {-1, 1}}],  {a, -4.1, 5.2414, 0.000001}]

But what I really need is to find a way to get a defined set of the admissible "a" parameter in the equation, instead of a graphic visualization.

Can please somebody help showing a suggestion or a way to do it?

Thank you very much! Rui.