I can't read your first equation. Is it ?
As for question 2, they all follow the same procedure. Do you understand how to find an integrating factor and use it to simplify a DE?
Q1.
A skydiver’s vertical velocity v is governed by the diﬀerential equation:
m
dv
dt = mg − Kv2
where m is the mass of the skydiver, g is the gravitational constant, and K > 0
is the drag coeﬃcient. If the skydiver leaves the airplane at time t = 0 with zero
vertical velocity, ﬁnd at what time she reaches half her ﬁnal velocity
Q2.
Solve the following problems by ﬁnding an integrating factor:
(a) dx/dt + 2x = e^−4t
(b) dx/dt −x/t = t^3 − 3, x(1) = −1
(c) t(dx/dt) + 4x = e^t
Any help or explanation would be appreciated. I have very little of an idea of how to approach these questions.