Imagine that you are launching an object through a mysterious wind tunnel in a cave system with the goal of modeling the velocity of the object as a function of time as it moves through the tunnel. For a variety of reasons, you cannot set up devices in the tunnel. You only have access to the position of the object over time via hardware installed on the object. At this point in your research, you are only interested in modeling the velocity of the object in the $x$ direction. The data that you have access to is shown in $$

Based on your research, you have two guesses for what the differential equations governing this behavior are:

$1.\{\begin{array}{c}\frac{dx}{dt}=v(t)\end{array}$

$\frac{dv}{dt}=\frac{a}{v(t{)}^2}-b$

$2.\{\begin{array}{c}\frac{dx}{dt}=v(t)\end{array}$

$\frac{dv}{dt}=\frac{a}{v(t{)}^2}-b**x(t)$

where a and $b$ are known coefficients.

In this exercise, you will determine which guess is correct.

Defining the Differential Equation Functions

Write a function guess$\_$ ime, $a,b$ which computes the derivative of $x$ at $t$ according to guess $1$ above.