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2001 II 2

< PlasmaWiki | Generals(Link to this page as [[PlasmaWiki/Generals/2001 II 2]])

The homogenous equation is:

$y^{\prime\prime}+\frac{y}{1+x}=0$

The approximate solution for $x\rightarrow\infty$ is:

$y_{h}=e^{\pm i\sqrt{1+x}}$

The full equation is:

$y^{\prime\prime}+\frac{y}{1+x}=x$

Guessing the balance for $y/\left(1+x\right)$ and $x$ , we get $y p = x + x 2$ . A check reveals that this is dominant. Then the general solution is:

$y=c_{1}\sin\left(\sqrt{1+x}\right)+c_{2}\cos\left(\sqrt{1+x}\right)+x+x^{2}$

This page was recovered in October 2009 from the Plasmagicians page on Generals_2001_II_2 dated 19:39, 25 April 2007.