Assume that needs to solved i.e. one needs to find for the initial condition . In your Math classes, you were taught how to solve this differential equation. However, most differential equations are not easily solvable and one needs to resort to numerical integration. This can easily be done in MATLAB for explicit first order differential equations like the one stated above. The time of interest is between, let's say between 0 and 2 seconds. Using the following MATLAB syntax, this will lead to a plot of the relationship:

y0 = 0.3;

timeSpan = [0 2];

[Time,Yout] = ode45(@(t,y)(y*t),timeSpan,y0);

plot(Time,Yout);

Now, assume a parachutist with a mass m of 80kg, a cross sectional area S of 0.65 m², a drag coefficient C_D = 0.45 at an atmospheric density at sea level = 1.225kg/m³ has an initial velocity of 0 m/s after dropping out of a balloon. Numerically solve the equation below, plot the velocity-time relationship and determine the terminal velocity. Also, discuss the formula with your peers. Can you find the terminal velocity analytically?

I'm stuck, please help me with this.