# DSolve bvlim error due to Boundary condition

I am solving an Ode using Mathematica: $$-p\alpha x^{p-1}=m\ddot{x},\quad x(0)=x_0,\quad x'(0)=x''(0)=0,\quad x(t_1)=0.$$ And I have $$p\alpha>0$$, all $$x$$ and $$t$$ are positive. I want to figure out $$t_1$$.

This is my code:

DSolve[
{(-p α/m) x[t]^(p - 1) == x''[t],
x == x0, x' == 0, x'' == 0, x[t1] == 0},
x[t], t,
Assumptions -> p α > 0 && p > 0 && m > 0 && t1 > 0 && x0 > 0
]


And the error message is

DSolve: General solution contains implicit solutions. In the boundary value problem, these solutions will be ignored, so some of the solutions will be lost.

How can I do?

• For second order diff equation DSolve can solve with only 2 initial/boundary condition. Mar 19 at 14:02
• Thank you! So which 2 of the initial conditions should I choose? Mar 19 at 14:06
• x'' is already given by the equation and can not be specified independently. But your problem is the term x[t]^(p - 1). Depending on p you can get many widely different solutions. You should set the exponent to a fixed value. Mar 19 at 14:09
• But p is an important factor in this problem. I’m afraid I can’t make it fixed. Mar 20 at 6:19