figure 1 diagram without and with gravity the models without and with

Question

Figure 1: Diagram without and with gravity
The models without and with gravity are illustrated in the figures above
for, and they can be described using the differential equations:
mv + um' = 0 and mv' +mg+um² = 0.
Solve both differential equations with respect to the speed v(t).
a) Without gravity. Solve the differential equation with respect to p'a the speed as a function of the mass.
b) With gravity. Solve the differential the speed as a function of time. equation with respect to p'a