# Thread: A Method for solving any differential equation

1. ## 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.

2. ## Re: A Method for solving any differential equation

Originally Posted by ysammour
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

3. ## 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.

Yousif

Yousif

6. ## 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?

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.

8. ## 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?

Yousif.

10. ## Re: A Method for solving any differential equation

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

"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,".

"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.

11. ## 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

12. ## 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.

13. ## Re: A Method for solving any differential equation

So this is NOT a "method solving any differential equation"?