Hi there,

So i have this question, where there is an infinite rope that is being stretched at 1000m/s, and is initially 1000m long (at t=0). A person is also walking along the rope at 1m/s as the rope is being stretched. The person is carried along with the rope as it stretches. I am then asked to show, without solving the DE, that my position x(t) satisfies the DE x'=1+x/(1+t), given the initial condition x(0)=0, where t is the time since the person started to walk along the rope.

So far, i have determined that the length of the rope at time t is 1000+1000t, but have no idea what else i can do to show that x(t) satisfies the DE.

How am i meant to show this without solving the differential equation for x(t) first? (I am asked to solve the DE in the next section).

Thanks in advance