Still celebrating National IT Professionals Day with 3 months of free Premium Membership. Use Code ITDAY17

x
Solved

question about Paul's Math website on linear diff. eq.

Posted on 2008-10-20
Medium Priority
396 Views
I'm looking at Paul's math page (Paul Dawkins of Lamar U) and on this page:
http://tutorial.math.lamar.edu/Classes/DE/Linear.aspx
about 1/2 down in example 1 he says:
Question:
dv/dt = 9.8 - 0.196v
Solution:
dv/dt + 0.196v = 9.8
u(t) = e^(integral(0.196dt)) = e^0.196t
OK, I get it so far - but how do they get from this:
e^(0.196t) dv/dt + 0.196e^(0.196t)v = 9.8e^(0.196t)
to this:
(e^(0.196t)v)' = 9.8e^(0.196t)

0
Question by:zliminator
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

• Help others & share knowledge
• Earn cash & points
1 Comment

LVL 16

Accepted Solution

Peter Kwan earned 1000 total points
ID: 22765169
Just follow the logic from equation 4 to equation 5, by substituting "u(t)" with e^0.196t and "y" with "v".

This is because d(e^ct)/dt = c * e^ct => d(e^0.196t)/dt = 0.196 * (e^0.196t)
0

Featured Post

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

This article seeks to propel the full implementation of geothermal power plants in Mexico as a renewable energy source.
This article provides a brief introduction to tissue engineering, the process by which organs can be grown artificially. It covers the problems with organ transplants, the tissue engineering process, and the current successes and problems of the tec…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…
Suggested Courses
Course of the Month9 days, 7 hours left to enroll