Recent content by joqhey

Well, guys, I did get a good calculator and was able to use my two formulae for exact solution of the Ricatti equation to reach the same result as wolfram did i.e y\left(2\right)=6.70378602229564586367. Great thanks to all of you. I was even able to come up with a graph that fits sufficiently...

I have just checked the Excel worksheet. It truncates all non-integral Bessel functions so that J_{\frac{1}{4}}=J_{\frac{3}{4}}=J_0. My bad. Sorry. Let me seek a different Besselcalculator. Thanks all.

I did take a look at the WolframAlpha solution. It seems that they took the solution into the more negative direction. As I'm using the basic Excel worksheet to solve the Bessel functions, I have been avoiding the differentiation that takes me to the more negative Bessel functions. This being...

I did take a look at the WolframAlpha solution. It seems that they took the solution into the more negative direction. As I'm using the basic Excel worksheet to solve the Bessel functions, I have been avoiding the differentiation that takes me to the more negative Bessel functions. This being...

Heres what I have done since (attached pdf). I know I shouldn't pursue it this long, but it is a good challenge. There are two possible solutions: a combination of Bessel J and Y, and a combination of Bessel J+ and J-. I worked them both out and if I didn't bungle it again, they neither match...

You are right, Jacquelin. Let me try that. I tried the solution suggested in the book "Handbook for Exact Solutions for Ordinary Differential Equations" in the combinations of J and Y functions I have worked with these suggested solutions and they don't look good either. Once I'm done I shall...

Thanks, JJacquelin, for the advice. I followed your method and have since posted a pdf of what I did. I do not know whether I messed it up since my exact solution is not even close to the Runge Kutta estimate. Please, check it out and advise me. Thank you again.

Thanks, Mute and Jacquelin for your support. The question was initially meant to be an easy exercise. However I have been on it since without much success. With your suggestions I was able to do the following. However my result, on comparison with the Runge Kutta estimate, does not look good...

I found this initial value problem and was supposed to comment on the accuracy of Runge Kutta method. Please enlighten me on the analytic solution. Find y(2) given the differential equation \frac{dy}{dx}=y^{2}+x^{2} and the initial value y(1)=0. Thank you.