Math Help Forum

Math Help Forum Feed Site Feed

Go Back   Math Help Forum > University Math Help > Calculus
Reply
 
Thread Tools Display Modes
  #1  
Old October 21st, 2007, 10:55 AM
Junior Member
 
Join Date: Sep 2007
Posts: 36
Country:
Thanks: 4
Thanked 1 Time in 1 Post
alikation0 is on a distinguished road
Default Cauchy-Euler Dif EQ

For a Cauchy Euler Dif EQ, its auxiliary equation for this Dif EQ:

at^2y'' + bty' + cy = g(t) is:

am^2 + (b-a)m + c = 0.

Use this auxiliary equation to solve the Cauchy-Euler equation below:

t^2y'' - 5ty' + 8y = 0 subject to y(2) = 32 and y'(2) = 0
Reply With Quote
Advertisement
 
  #2  
Old October 21st, 2007, 11:02 AM
topsquark's Avatar
Generous Contributor
 
Join Date: Jan 2006
Location: Angelica, NY
Posts: 7,618
Country:
Thanks: 643
Thanked 2,312 Times in 2,098 Posts
topsquark has a reputation beyond reputetopsquark has a reputation beyond reputetopsquark has a reputation beyond reputetopsquark has a reputation beyond reputetopsquark has a reputation beyond reputetopsquark has a reputation beyond reputetopsquark has a reputation beyond reputetopsquark has a reputation beyond reputetopsquark has a reputation beyond reputetopsquark has a reputation beyond reputetopsquark has a reputation beyond repute
Default

Quote:
Originally Posted by alikation0 View Post
For a Cauchy Euler Dif EQ, its auxiliary equation for this Dif EQ:

at^2y'' + bty' + cy = g(t) is:

am^2 + (b-a)m + c = 0.

Use this auxiliary equation to solve the Cauchy-Euler equation below:

t^2y'' - 5ty' + 8y = 0 subject to y(2) = 32 and y'(2) = 0
Well, a = 1, b = -5 and c = 8, so the auxiliary equation becomes
m^2 - 6m + 8 = 0

(m - 2)(m - 4) = 0

So m = 2 and m = 4.

Thus the most general solution to this equation is
y = Ax^2 + Bx^4

-Dan
__________________
Got a Physics question? Come on over to
To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.

To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.


"I must not fear. Fear is the mind killer. Fear is the little death that brings total obliteration. I will face my fear. I will permit it to pass over me and through me. And when it has gone I will turn the inner eye to see its path. Where the fear has gone there will be nothing. Only I will remain." - The Litany Against Fear, "Dune" by Frank Herbert
Reply With Quote
  #3  
Old October 21st, 2007, 12:50 PM
ThePerfectHacker's Avatar
Global Moderator

 
Join Date: Nov 2005
Location: New York City
Posts: 11,177
Country:
Thanks: 482
Thanked 3,779 Times in 3,073 Posts
ThePerfectHacker has a reputation beyond reputeThePerfectHacker has a reputation beyond reputeThePerfectHacker has a reputation beyond reputeThePerfectHacker has a reputation beyond reputeThePerfectHacker has a reputation beyond reputeThePerfectHacker has a reputation beyond reputeThePerfectHacker has a reputation beyond reputeThePerfectHacker has a reputation beyond reputeThePerfectHacker has a reputation beyond reputeThePerfectHacker has a reputation beyond reputeThePerfectHacker has a reputation beyond repute
Default

If you want a solution on (0,\infty) then it is like topsquark said. If you want a solution on the open set (-\infty,0)\cup (0,\infty) then it is A|x|^2+B|x|^4.
__________________

To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.


"Democracy has proved only that the best way to gain power
over people is to assure the people that they are ruling
themselves. Once they believe that, they make wonderfully
submissive slaves." - Joseph Sobran


To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
Reply With Quote
Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are Off
Refbacks are Off
Forum Jump


All times are GMT -7. The time now is 05:07 AM.


Powered by vBulletin® Version 3.7.3
Copyright ©2000 - 2010, Jelsoft Enterprises Ltd.
SEO by vBSEO 3.2.0 ©2008, Crawlability, Inc.
©2005 - 2009 Math Help Forum


Math Help Forum is a community of maths forums with an emphasis on maths help in all levels of mathematics.
Register to post your math questions or just hang out and try some of our math games or visit the arcade.