Results 1 to 4 of 4

Math Help - differential equations

  1. #1
    Junior Member
    Joined
    Mar 2008
    Posts
    45

    differential equations

    Hi all,

    I need help solving for this:
    <br />
\int \frac{du}{3u + \sqrt{u}} = \int \frac{dx}{x}<br />

    Thanks in advance
    ArTiCk
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by ArTiCK View Post
    Hi all,

    I need help solving for this:
    <br />
\int \frac{du}{3u + \sqrt{u}} = \int \frac{dx}{x}<br />

    Thanks in advance
    ArTiCk
    Let \xi=\sqrt{u}\Rightarrow{\xi^2=u}

    So du=2\xi{d\xi}

    So we have

    \int\frac{2\xi}{3\xi^2+\xi}d\xi=\frac{2\ln(3\xi+1)  }{3}

    back subbing we get

    \frac{2\ln(3\sqrt{u}+1)}{3}=\ln((3\sqrt{u}+1)^{\fr  ac{2}{2}})

    The right side is obviously \ln(x)

    so we have

    \ln((3\sqrt{u}+1)^{\frac{2}{3}})=\ln(x)

    exponentiating both sides gives

    (3\sqrt{u}+1)^{\frac{2}{3}}=x


    and I assume this was solving for x

    so done
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,678
    Thanks
    610
    Hello, ArTiCK!

    \int \frac{du}{3u + \sqrt{u}} \:= \:\int \frac{dx}{x}
    Let \sqrt{u} \,=\,v\quad\Rightarrow\quad u \,=\,v^2\quad\Rightarrow\quad du \,=\,2v\,dv

    Substitute: . \int\frac{2v\,dv}{3v^2+v} \;=\;\int\frac{dx}{x} \quad\Longrightarrow\quad 2\int\frac{dv}{3v+1} \:=\:\int\frac{dx}{x}

    Go for it!

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    Isomorphism also said few words here.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. 'Differential' in differential equations
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: October 5th 2010, 10:20 AM
  2. Replies: 2
    Last Post: May 18th 2009, 03:49 AM
  3. Differential Equations
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 12th 2009, 05:44 PM
  4. Replies: 5
    Last Post: July 16th 2007, 04:55 AM
  5. Replies: 3
    Last Post: July 9th 2007, 05:30 PM

Search Tags


/mathhelpforum @mathhelpforum