Someone2841
New member
- Joined
- Sep 7, 2011
- Messages
- 35
I have been interested for a while now in the differential equation x''(t) = -1/x(t)2 where x(0) = h and x'(0) = 0. I've only made limited progress on this, and recently have been looking into a more specific case where x(0) = -1.
When x(0) = h, the solution for x'(t) is x'(t) = sqrt(1/x(t) - 1/h), which can be easily verified via implicit differentiation.
When h = -1, x'(t) =
I would like to find the explicit form (in terms of elementary or special functions) of x(t). So far I have hit a dead end at:
t = integral{1/sqrt[(x(t)+1)/x(t)]}dx(t), which after integrating would give at best an implicit solution.
Any ideas/suggestions?
When x(0) = h, the solution for x'(t) is x'(t) = sqrt(1/x(t) - 1/h), which can be easily verified via implicit differentiation.
When h = -1, x'(t) =
I would like to find the explicit form (in terms of elementary or special functions) of x(t). So far I have hit a dead end at:
t = integral{1/sqrt[(x(t)+1)/x(t)]}dx(t), which after integrating would give at best an implicit solution.
Any ideas/suggestions?