Results 1 to 5 of 5

Math Help - Differential equations problem (easy?)

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    26

    Differential equations problem (easy?)

    do u know how to solve this : u'' + 1/r u' = 0 (i forgot the method and i don't have my notebook)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by tom007 View Post
    do u know how to solve this : u'' + 1/r u' = 0 (i forgot the method and i don't have my notebook)
    This is a Cauchy-Euler equation. Multiply through by r^2, to get r^2u'' + ru' = 0.

    Now, go to Chris' differential equations tutorial (link in my signature) and see post #5
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member DeMath's Avatar
    Joined
    Nov 2008
    From
    Moscow
    Posts
    473
    Thanks
    5
    Quote Originally Posted by tom007 View Post
    do u know how to solve this : u'' + 1/r u' = 0 (i forgot the method and i don't have my notebook)
    Multiply by r

    u'' + \frac{u'}{r} = 0 \Leftrightarrow ru'' + u' = 0 \Leftrightarrow \left(ru'\right)^\prime = 0 \Rightarrow ru' = C_1 \Leftrightarrow u' = \frac{C_1}<br />
{r} \Rightarrow u = C_1\ln|r| + C_2.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by DeMath View Post
    Multiply by r

    u'' + \frac{u'}{r} = 0 \Leftrightarrow ru'' + u' = 0 \Leftrightarrow \left(ru'\right)^\prime = 0 \Rightarrow ru' = C_1 \Leftrightarrow u' = \frac{C_1}<br />
{r} \Rightarrow u = C_1\ln|r| + C_2.
    even better!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jan 2010
    Posts
    26
    Quote Originally Posted by DeMath View Post
    Multiply by r

    u'' + \frac{u'}{r} = 0 \Leftrightarrow ru'' + u' = 0 \Leftrightarrow \left(ru'\right)^\prime = 0 \Rightarrow ru' = C_1 \Leftrightarrow u' = \frac{C_1}<br />
{r} \Rightarrow u = C_1\ln|r| + C_2.
    yeea..now i remember!!! tnx!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Differential Equations problem
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: March 23rd 2010, 07:20 AM
  2. differential equations problem
    Posted in the Differential Equations Forum
    Replies: 9
    Last Post: October 5th 2009, 05:46 PM
  3. Replies: 9
    Last Post: April 23rd 2009, 11:46 PM
  4. Replies: 1
    Last Post: February 11th 2009, 01:58 PM
  5. Differential Equations Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 6th 2008, 06:05 AM

Search Tags


/mathhelpforum @mathhelpforum