Results 1 to 7 of 7

Math Help - First order differential equation

  1. #1
    Newbie
    Joined
    May 2012
    From
    Sweden
    Posts
    10

    First order differential equation




    find the solution that fulfills


    please take me through the steps cause i dont know where to start all i can see is that it is separable and i didnt get how to solve it by reading in the book or solving the easier ones
    Last edited by joceninja; May 21st 2012 at 11:53 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Sylvia104's Avatar
    Joined
    Mar 2012
    From
    London, UK
    Posts
    107
    Thanks
    37

    Re: First order differential equation

    e^{2y}\frac{\mathrm dy}{\mathrm dx} = x+x^3

    \Rightarrow\ \int e^{2y}\,\mathrm dy = \int x+x^3\,\mathrm dx
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2012
    From
    Sweden
    Posts
    10

    Re: First order differential equation

    Quote Originally Posted by Sylvia104 View Post
    e^{2y}\frac{\mathrm dy}{\mathrm dx} = x+x^3

    \Rightarrow\ \int e^{2y}\,\mathrm dy = \int x+x^3\,\mathrm dx

    im with you so far but i dont see how im supposed to solve the
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member Sylvia104's Avatar
    Joined
    Mar 2012
    From
    London, UK
    Posts
    107
    Thanks
    37

    Re: First order differential equation

    Do the integration first.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2012
    From
    Sweden
    Posts
    10

    Re: First order differential equation



    like that or?
    feels like im wrong cause i never really understood what you do when you take the dy/dx and take *dy on both sides so you get dy on left side and dx on right side etc.

    cause i dont see how dy and dx just can move around since dy/dx=y'
    Last edited by joceninja; May 21st 2012 at 12:27 PM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member Sylvia104's Avatar
    Joined
    Mar 2012
    From
    London, UK
    Posts
    107
    Thanks
    37

    Re: First order differential equation

    \int e^{2y}\,\mathrm dy = \int x+x^3\,\mathrm dx

    \Rightarrow\ \frac{e^{2y}}2 = \frac{x^2}2 + \frac{x^4}4 + C

    Now substitute x=0,y=0 to find the constant C.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    May 2012
    From
    Sweden
    Posts
    10

    Re: First order differential equation

    ahh ye my bad this is where i made the misstake e^(2y)

    but cheers for the help!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: September 21st 2011, 04:37 PM
  2. [SOLVED] First order differential equation
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: July 4th 2011, 07:54 AM
  3. first order differential equation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 1st 2009, 02:17 PM
  4. Replies: 2
    Last Post: November 25th 2008, 10:29 PM
  5. First order differential equation
    Posted in the Calculus Forum
    Replies: 9
    Last Post: April 5th 2008, 04:08 PM

Search Tags


/mathhelpforum @mathhelpforum