1. The problem statement, all variables and given/known data At what time does the particle reach infinity given that H(p,x)=(1/2)p^2 -(1/2)x^4. And initial values are x(0)=1 and p(0)=1 2. Relevant equations The hamiltonian equations i believe are given by the partial derivatives let d mean partial derivative so x'=dH/dp and p'=-dH/dx 3. The attempt at a solution well so far i have that x'=p and p'=2x^3 but at this point, im confused over how to impose the initial values... This is my attempt. By seperation of variables, dx/dt=p so (1/p)x=t+ c by integration and now i impose initial value of x(0)=1which gives me c=1/p so i get t=(1/p)x-(1/p) and for dp/dt i got t=(1/2x^3)p - (1/2x^3) . At this point im very confused what to do next or if im doing this right in the first place... How can i tell when the particle reaches infinity with two times??