Question

The motion of a set of particles moving along the x-axis is governed by the differential equation; dt/dx t^3-x^3,where x(t) denotes the position at time t of the particle.

Show that the acceleration of a particle is given by d^2x/dt^2=3t^2-3t^33x^2 +3x^5 .

If a particle is located as x=2 when t=2.5 can it reach the location x=1 at any later time?