Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By SlipEternal

Thread: Does this differential equation have very lengthy solution?

  1. #1
    Senior Member Vinod's Avatar
    Joined
    Sep 2011
    From
    Mumbai (Bombay),Maharashtra,India
    Posts
    321
    Thanks
    5

    Does this differential equation have very lengthy solution?

    Hello,
    $\frac{dy}{dx}=\frac{x+1}{y(y+2)}$

    Solution: $(y^2+2y)dy=(x+1)dx$

    Integrating both the sides, we get
    $\frac{(y^3+3y^2)}{3}=\frac{(x^2+2x)}{2}+c$

    Now here i am stuck. When i put this differential equation in wolfram alpha it gave me very lengthy solution.Now what should i do?
    Last edited by Vinod; Jun 25th 2018 at 05:23 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2010
    Posts
    3,636
    Thanks
    1460

    Re: Does this differential equation have very lengthy solution?

    You forgot the $+C$. Other than that, if you are looking to get $y$ in terms of $x$, it is not possible with a single formula. You have a cubic polynomial in $y$, so when you solve the cubic, you will have three solutions, and those solutions are not "pretty". I recommend stopping when you get to the step you are currently on (after adding the missing $+C$). There is no need to find an explicit formula for $y$. You did your due diligence and simplified it as much as is needed.
    Thanks from Vinod
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: May 28th 2016, 12:45 AM
  2. differential equation solution
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: Sep 29th 2010, 03:04 AM
  3. Differential equation solution
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: Aug 26th 2010, 06:47 AM
  4. Particular Solution to Differential Equation!!!
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: May 29th 2009, 12:14 PM
  5. solution of a differential equation
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: Nov 7th 2008, 07:18 PM

/mathhelpforum @mathhelpforum