User:GFauxPas/Sandbox

Welcome to my sandbox, you are free to play here as long as you don't track sand onto the main wiki. --GFauxPas 09:28, 7 November 2011 (CST)

DiffEQ Ongoing Project
Assignment:


 * $\displaystyle \int_{\to 0}^{\to 1} \ln x \ln \left({1-x}\right)\ \mathrm dx$

Use the taylor series expansion of $\ln (1-x)$ but not of $\ln x$

--GFauxPas (talk) 21:13, 10 March 2014 (UTC)

diff eq
Do we have this on PW?

Let


 * $\dfrac {\mathrm dy}{\mathrm dx} = f\left({x,y}\right)$

Let $f$ be expressible i.t.o. $\dfrac y x$. Then letting $v = \dfrac y x$ will result in:


 * $\dfrac {\mathrm dy}{\mathrm dx} = x \dfrac {\mathrm dv}{\mathrm dx} + v$

which is separable.

Does this method have a name? --GFauxPas (talk) 17:50, 18 March 2014 (UTC)


 * Yes we do: Solution to Homogeneous Differential Equation.--prime mover (talk) 07:20, 19 March 2014 (UTC)


 * Great, thanks. --GFauxPas (talk) 12:21, 19 March 2014 (UTC)