# Integrating factor and differential equation questions help

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• March 24th 2013, 04:14 PM
JoshuaJava
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.
• March 25th 2013, 12:41 AM
Prove It
Re: Integrating factor and differential equation questions help
I can't read your first equation. Is it $\displaystyle \frac{dv}{dt} = m\,g - k\,v^2$?

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?
• March 25th 2013, 04:11 PM
JoshuaJava
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