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December 6th, 2017, 06:02 PM   #1
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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.
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December 6th, 2017, 06:15 PM   #2
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Originally Posted by Albert Do View Post
$\displaystyle y''+(3x^2-1/x)y'=A/x$

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.
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December 6th, 2017, 06:38 PM   #3
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Use $\displaystyle \frac{e^{\Large x^{\Large3}}}{x}$ as an integrating factor.
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December 13th, 2017, 05:37 AM   #4
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Do you mean $\displaystyle 3x^2- 1/x$ (what you wrote) or $\displaystyle (3x^2- 1)/x$?
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December 13th, 2017, 06:15 AM   #5
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Reduce the order by writing $v=y'$.
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