Show that question

Show that question

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).

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Re: Show that question

"Without solving" what differential equation "first"? This problem is just asking you to write the differential equation itself. Then, as you say, the next problem asks you to solve it.
Guest