Integrating factor and differential equation questions help

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.

Re: Integrating factor and differential equation questions help

I can't read your first equation. Is it $\displaystyle \displaystyle \frac{dv}{dt} = m\,g - k\,v^2 $?

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?

Re: Integrating factor and differential equation questions help

Hi, sorry it's m(dv/dt) = mg - kv^2. And no, I basically dont understand how to use the integrating factor