Results 1 to 5 of 5

Math Help - Simple differential equation

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    22

    Simple differential equation

    Find a family of solutions to the DE dy/dx+ 2xy=1

    I have some trouble separating the variables...anyone can give me a general method on how to do that?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    The trouble is this is not a separable equation.

    You have to use an integrating factor .

    Do you know this method ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    22
    oh sorry let me rephrase the question:

    Verify that the indicated family of functions is a solution to the DE dy/dx+2xy=1:

    y= (e^-x^2)*integral from x to 0 (e^(t^2)dt)+ce^(-x^2)

    where c is an arbitrary constant.
    I suppose the e^t^2 is the integrating factor??
    I tried to substitute the y equation into the DE but it does not work.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    See the attachment



    By the way The integrating factor would be e^(x^2) but you'll get to that later I assume
    Attached Thumbnails Attached Thumbnails Simple differential equation-diffeq.jpg  
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    If You write the DE as...

    y^{'} = -2xy +1 (1)

    ... it is easy to see that it's a linear DE on the form...

    y^{'} = a(x)\cdot y +b(x) (2)

    ... where a(x)= -2x and b(x)=1 and its solution can be found is 'standard fashion' ...

    y= e^{\int a(x)\cdot dx} \{\int b(x)\cdot e^{-\int a(x)\cdot dx }\cdot dx +c\} = e^{-x^{2}}\cdot (\int e^{x^{2}}\cdot dx + c) (3)

    The integral in (3) is not elementary but it can be expressed as a convergent series...

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. simple differential equation
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: June 28th 2009, 04:45 PM
  2. Very simple differential equation
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 18th 2008, 05:13 PM
  3. simple differential equation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 17th 2008, 01:06 AM
  4. simple differential equation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 18th 2007, 12:13 PM
  5. A simple differential equation.
    Posted in the Calculus Forum
    Replies: 7
    Last Post: September 11th 2007, 04:33 PM

Search Tags


/mathhelpforum @mathhelpforum