I'm trying to solve a third-order nonlinear ordinary differential equation. I couldn't get the answer even using Mathematica. The equation is: u'''(t) + u/2 u''(t) = 0 with conditions u(0)=0, u'(0)=0, u(10)=1. I need to get both analytic solution and numerical solution. For the numerical solution, I'm thinking the Newton iterative algorithm. But for the analytic solution, I really have no idea.