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.