Results 1 to 3 of 3

Math Help - integration -- getting constants

  1. #1
    Junior Member
    Joined
    Oct 2010
    Posts
    39

    integration -- getting constants

    On this page below, the person chooses the constants to be anything they want, but can you actually do that?
    Pauls Online Notes : Differential Equations - Reduction of Order
    Attached Thumbnails Attached Thumbnails integration -- getting constants-12345.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Mar 2010
    Posts
    280
    <br />
 \displaystyle { <br />
y_1=\frac{1}{t}<br />
}<br />

    <br />
 \displaystyle { <br />
y_2=y_1 \; \nu<br />
}<br />

    <br />
\displaystyle { \nu=\frac{2}{5}c t^{5/2}+k<br />
}<br />

    <br />
\displaystyle { <br />
y_2=t^{-1} \nu=\frac{2}{5}c t^{3/2}+\frac{k}{t}<br />
}<br />

    <br />
\displaystyle { <br />
y=c_1 y_1+c_2 y_2=c_1 \frac{1}{t} +c_2\frac{2}{5}ct^{3/2}+\frac{kc_2}{t}=\frac{1}{t}(c_1+kc_2)+c_2 \frac{2}{5} c t^{3/2}=c_1' \frac{1}{t}+c_2't^{3/2}.<br />
}<br />
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Dec 2009
    From
    1111
    Posts
    872
    Thanks
    3
    Quote Originally Posted by rlkmg View Post
    On this page below, the person chooses the constants to be anything they want, but can you actually do that?
    Pauls Online Notes : Differential Equations - Reduction of Order
    Dear rlkmg,

    c and k are arbitary constants which came up as a result of integration. Note that if you have a function f(x) which is differentiable, then \frac{d}{dx}\left[f(x)+C\right]=g(x) where C is any constant value. Therefore \int{g(x)}dx=f(x)+C

    Hope you get the idea.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: June 12th 2011, 03:40 AM
  2. Ricatti Equations and combining integration constants.
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: April 24th 2011, 05:34 AM
  3. Replies: 5
    Last Post: November 23rd 2009, 12:17 PM
  4. constants of D.e
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 10th 2008, 11:32 PM
  5. ode's and constants
    Posted in the Calculus Forum
    Replies: 7
    Last Post: February 7th 2007, 07:34 AM

Search Tags


/mathhelpforum @mathhelpforum