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1

You can help Mathematica a bit . Express all terms that contain θ23 through an abbreviation variable called s (reminding of the Sin function) to prevent all sorts of trigonometric transformations happening to Sin[θ23 Degree] while trying to solve for it. eq=(2 Exp[-I δ Degree] Sec[θ12 Degree]^2 (-(1/4) Exp[2 I δ Degree] (7 + Cos[8 θ12 Degree]) Cos[θ23 ...

2

surf1[a_, b_] = ContourPlot3D[ y^2/a^2 + z^2/b^2 == 1, {x, -5, 5}, {y, -5, 5}, {z, -5, 5}, RegionFunction -> Function[{x, y, z}, z^2/b^2 + x^2/a^2 >= 1 && z >= 0 && Abs[x] <= Min[a, b] && Abs[y] <= Min[a, b]], PlotPoints -> 50, RegionBoundaryStyle -> None, Mesh -> None]; surf2[a_,...

2

One approach is to find the zero of Reduce[D[q ((-Log[1 - q])^-a - (-Log[q])^-a)/a, q] == 0 && 0 < q < 1, q, Reals] but it returns unevaluated, suggesting that there is no symbolic solution. In the absence of a symbolic solution, a numeric solution can be obtained quickly with, Plot[NMaxValue[{(q ((-Log[1 - q])^-a - (-Log[q])^-a))/a, 0 < q ...

3

It appears that Mathematica cannot integrate the ODE all the way from -1 to 1 for certain values of $a$. The important error messages that are returned are ParametricNDSolveValue::ndsz: At x\$8411 == -0.760075, step size is effectively zero; singularity or stiff system suspected. NMinimize::nnum: The function value (-0.2+NIntegrate[paraNDsol[0.747922][x],{...

4

but without hardcoding? First of all, line[t_] = {t, 2t, 3t} is not an equation. Equation should have == in it. This is function definition. Second, better to use delayed := instead of immediate = when making functions, unless there is a good reason to use immediate definition. I do not know why you do not want to do normal explicit definitions for x[t_] ...

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