I am trying to draw a surface of revolution recovered from a differential equation with a singularity. In the simplest case, the answer is a sphere. You can check by hand. I manage to draw 2 dimensional plot but the 3 dimensional plot doesn't work.

e = 0.0001; NDSolve[{Sqrt[1 + (u'[t])^2] == 1/(Sqrt[1 - t^2]), u[0.9999999] == 0}, u, {t, e, 1 - e}] Plot[Evaluate[u[t] /. %], {t, e, 1 - e}, PlotRange -> All, AspectRatio -> Automatic]

--works

RevolutionPlot3D[Evaluate[u[t] /. %], {t, e, 1 - e}]

--doesn't work

What is the major difference? Do you have any idea how to fix it?

Thank you

I am trying to draw a surface of revolution recovered from a differential equation with a singularity. In the simplest case, the answer is a sphere. You can check by hand. I manage to draw 2 dimensional plot but the 3 dimensional plot doesn't work.

e = 0.0001;
NDSolve[{Sqrt[1 + (u'[t])^2] == 1/(Sqrt[1 - t^2]), u[0.9999999] == 0}, u, {t, e, 1 - e}]
Plot[Evaluate[u[t] /. %], {t, e, 1 - e}, PlotRange -> All, AspectRatio -> Automatic]

--works

RevolutionPlot3D[Evaluate[u[t] /. %], {t, e, 1 - e}]

--doesn't work

What is the major difference? Do you have any idea how to fix it?

Thank you