Results 1 to 7 of 7

Math Help - Differential Equation 1

  1. #1
    Super Member
    Joined
    Oct 2006
    Posts
    679
    Awards
    1

    Differential Equation 1

    Thanks!!
    Attached Thumbnails Attached Thumbnails Differential Equation 1-73.gif  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,802
    Thanks
    691
    Hello, qbkr21!

    (x^2+1)\frac{dy}{dx} \:=\:xy
    Separate the variables . . . x's on one side, y's on the other.

    . . . \frac{dy}{y} \:=\:\frac{x}{x^2+1}\,dx

    Then integrate: . \int\frac{dy}{y} \;=\;\int\frac{x}{x^2+1}\,dx


    Can you finish it now?

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    Quote Originally Posted by qbkr21 View Post
    May I ask... what does mean the dt over there?, we just define y'=\frac{dy}{dx}.

    --

    Remember the useful trick \int\frac{f'(x)}{f(x)}\,dx=\ln|f(x)|+k,\,\forall f(x)>0.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Oct 2006
    Posts
    679
    Awards
    1

    Re:

    Re:
    Attached Thumbnails Attached Thumbnails Differential Equation 1-75.gif  
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    It is faster if you define the constant as \ln|c|, 'cause it's arbitrary.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Oct 2006
    Posts
    679
    Awards
    1

    Re:

    Quote Originally Posted by Krizalid View Post
    It is faster if you define the constant as \ln|c|, 'cause it's arbitrary.
    Example? I don't understand ...

    Thanks
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    Quote Originally Posted by Soroban View Post
    Then integrate: . \int\frac{dy}{y} \;=\;\int\frac{x}{x^2+1}\,dx
    To qbkr21:

    Let's check this.

    Integratin' we have \ln|y|=\frac12\ln(x^2+1)+c_1

    Since the constant is arbitrary, we may set it as \ln|c|\implies\ln|y|=\frac12\ln(x^2+1)+\ln|c|.

    Now apply properties of logs. and you're done.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Partial Differential Equation satisfy corresponding equation
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: May 16th 2011, 07:15 PM
  2. Replies: 4
    Last Post: May 8th 2011, 12:27 PM
  3. Replies: 1
    Last Post: April 11th 2011, 01:17 AM
  4. [SOLVED] Solve Differential equation for the original equation
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: February 21st 2011, 01:24 PM
  5. Partial differential equation-wave equation - dimensional analysis
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: August 28th 2009, 11:39 AM

Search Tags


/mathhelpforum @mathhelpforum