Results 1 to 13 of 13
Like Tree5Thanks
  • 1 Post By topsquark
  • 1 Post By HallsofIvy
  • 2 Post By Archie
  • 1 Post By topsquark

Thread: A Method for solving any differential equation

  1. #1
    Newbie
    Joined
    Dec 2015
    From
    Jeddah - Saudi Arabia
    Posts
    7

    A Method for solving any differential equation

    Hi,
    This is a method for solving differential equations of any order and any degree. Please go to this website to see how:
    http://www.sysins.com
    Thanks.
    Yousif Sammour.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    11,245
    Thanks
    762
    Awards
    1

    Re: A Method for solving any differential equation

    Quote Originally Posted by ysammour View Post
    Hi,
    This is a method for solving differential equations of any order and any degree. Please go to this website to see how:
    http://www.sysins.com
    Thanks.
    Yousif Sammour.
    Looks very nice. But what if you don't have a linear equation? Such as $\displaystyle \frac{dy}{dx} = xy^2$ for example. It's separable but it doesn't look like your method would cover it.

    -Dan
    Thanks from ysammour
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Dec 2013
    From
    Colombia
    Posts
    1,915
    Thanks
    642

    Re: A Method for solving any differential equation

    This is essentially the same as the standard way of finding power series solutions of a differential equation, except that you don't need to know the approximate form of the series beforehand.

    But I'm not sure that represents any great advance.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Dec 2015
    From
    Jeddah - Saudi Arabia
    Posts
    7

    Re: A Method for solving any differential equation

    Dan I appreciate your reply ... section 5 talks about non-linear differential equations ... Thanks.
    Yousif
    Last edited by ysammour; Apr 24th 2018 at 03:48 AM. Reason: misplaced
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Dec 2015
    From
    Jeddah - Saudi Arabia
    Posts
    7

    Re: A Method for solving any differential equation

    Archie Thanks for your reply
    Yousif
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,926
    Thanks
    3098

    Re: A Method for solving any differential equation

    In section 5 you give one example of a non-linear equation, $\displaystyle \left(\frac{dy}{dx}\right)+ y= x$, giving the solution as $\displaystyle y= ...\int\left(x- \int\left(x- \frac{2}{3}x^{\frac{3}{2}}\right)^{\frac{1}{2}}dx \right)^{\frac{1}{2}}dx$.

    But then you say "I did not check this solution"! Why not? How can you assert that your method works for any equation if you haven't checked for this equation? What does the "..." mean?
    Last edited by topsquark; Apr 27th 2018 at 09:38 AM. Reason: Tweaked LaTeX
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Dec 2015
    From
    Jeddah - Saudi Arabia
    Posts
    7

    Re: A Method for solving any differential equation

    Hello HallsofIvy,
    I found the first root and I checked it and it was OK. the second root is what I said about it "I did not check this solution" because it needs help from every body to check if interested because the whole paper idea is new and no previous research was carried out on it. the "..." means "more terms".
    Thanks.
    Yousif.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Dec 2013
    From
    Colombia
    Posts
    1,915
    Thanks
    642

    Re: A Method for solving any differential equation

    That's not how research works. If you want to be taken seriously, you check all of your own work. If it's interesting enough, people might then read it and even confirm it (or point out errors). But if you can't be bothered to check it, why should anyone else?
    Thanks from topsquark and ysammour
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Dec 2015
    From
    Jeddah - Saudi Arabia
    Posts
    7

    Re: A Method for solving any differential equation

    Archie Thanks for your reply
    Yousif.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Dec 2015
    From
    Jeddah - Saudi Arabia
    Posts
    7

    Re: A Method for solving any differential equation

    As per your replies and directions gentlemen, I updated the following:

    1- instead of:
    "5. Solving non-linear differential equations
    Solving a non-linear differential equation is like solving a polynomial, so at the beginning we will solve a polynomial. Let’s start by solving the following quadratic equation,"
    I changed it to be:
    "5. Solving simple non-linear differential equations
    Solving a non-linear differential equation is like solving a polynomial, so at the beginning we will solve a polynomial. This method solves simple non-linear differential equations. solving non-linear differential equations using this method requires more research. Let’s start by solving the following quadratic equation,".

    2- instead of:
    "I did not check this solution. But if the solution is divergent or is identical to the first root, then you need to change the structure of the differential equation to get the second root as I have done with the quadratic equation."
    I changed it to be:
    "I did not check the convergence of this second root. But if the solution is divergent or is identical to the first root, then you need to change the structure of the differential equation to get the second root as I have done with the quadratic equation in section 5.1. checking the convergence of this root is hard. the whole subject of non-linear differential equations requires extensive research."

    Thanks to all of your good selves.

    Yousif.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    11,245
    Thanks
    762
    Awards
    1

    Re: A Method for solving any differential equation

    Sorry to bug you about this but I still don't see how to solve $\displaystyle \frac{dy}{dx} = xy^2$. Could you please show how you would do this?

    Thanks.

    -Dan
    Thanks from ysammour
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Newbie
    Joined
    Dec 2015
    From
    Jeddah - Saudi Arabia
    Posts
    7

    Re: A Method for solving any differential equation

    Hello Dan,
    You are right, such equation in its shape can't be solved by the process of calculate and balance I have in my method ... there should be a free term to be able to solve it, like for example dy/dx-xy2=f(x) and f(x) should be specified ie x or x2-5.

    Thanks.

    Yousif.
    Follow Math Help Forum on Facebook and Google+

  13. #13
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,926
    Thanks
    3098

    Re: A Method for solving any differential equation

    So this is NOT a "method solving any differential equation"?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Which method for solving this form of differential equation?
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: Oct 30th 2012, 01:23 PM
  2. Replies: 2
    Last Post: Mar 12th 2012, 01:25 AM
  3. Solving differential equation by Frobenius method.
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: Jul 3rd 2010, 05:04 AM
  4. Which Differential Equation Method Do I use?
    Posted in the Differential Equations Forum
    Replies: 7
    Last Post: May 23rd 2010, 12:23 PM
  5. Replies: 1
    Last Post: Nov 11th 2009, 07:46 PM

/mathhelpforum @mathhelpforum