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 December 6th, 2017, 06:02 PM #1 Newbie   Joined: Dec 2017 From: Malaysia Posts: 1 Thanks: 0 Need help for this expression $\displaystyle y''+(3x^2-1/x)y'=A/x$ Any method can be used to solve this equation? Thanks a lot.
December 6th, 2017, 06:15 PM   #2
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 Originally Posted by Albert Do $\displaystyle y''+(3x^2-1/x)y'=A/x$ Any method can be used to solve this equation? Thanks a lot.
Maybe Fronenius method with A=0, then variation of parameters for particular solution.

There might be a nice substitution that I can't see though.

 December 6th, 2017, 06:38 PM #3 Global Moderator   Joined: Dec 2006 Posts: 18,248 Thanks: 1439 Use $\displaystyle \frac{e^{\Large x^{\Large3}}}{x}$ as an integrating factor. Thanks from Joppy
 December 13th, 2017, 05:37 AM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,875 Thanks: 766 Do you mean $\displaystyle 3x^2- 1/x$ (what you wrote) or $\displaystyle (3x^2- 1)/x$?
 December 13th, 2017, 06:15 AM #5 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,091 Thanks: 2360 Math Focus: Mainly analysis and algebra Reduce the order by writing $v=y'$.

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