We will develop a differential equation modeling the launch of Falcon 9 produced by Space X. This two-stage rocket has a mass 5.5105kg, and will be powered at the first stage by 9 Merlin engines that altogether produces a total thrust about 7.6105kg. The nine engines running at this thrust level burn about 1.45103kg of fuel and oxygen per second. The air resistance on the rocket may be modeled using either linear or quadratic relation fa=lv,fa=qv2 with the linear coefficient l=50 or the quadratic coefficient q=1.87 if the velocity is in m/s (meter/second) and the force is in N (Newton). All these numbers are approximated but pretty physical. We only consider the motion of the rocket prior to the first stage shutdown. (1) Write down the expressions of instantaneous mass of the rocket and the total force on the rocket. (2) Write down the two differential equations based on the Newton' second law respectively using linear and nonlinear resistance model. (3) Determine whether the equations are linear or nonlinear, separable or non-separable, homogeneous or inhomogeneous, autonomous or non-autonomous, and exact or non-exact. (4) Analytically solve the equation with linear resistance model. You may work on the equation with letter variables only. (5) Write MATLAB code to numerically solve both equations on time interval [0,T]. Properly select initial conditions, the terminal time T, and the time increments. Justify your selections. Plot the solutions using dotted lines and mark corresponding air resistance model of each solution, and submitted the printed figures