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I'm having a really hard time solving

$xy'' + 2y' + 4xy = 0$

I basically tried a lot of substitutions and series but couldn't find it. I realize this isn't as hard as I make it out to be so I'm assuming there is a certain trick that I am not seeing.

Thanks in advance!

  • 0
    Have you seen $y''+p(x)y'+q(x)y=0$ before?2011-12-11

2 Answers 2

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Let be $z = xy$. We have z''= 2y' + xy'' e the equation becomes z'' + 4 z = 0

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Simply use the Taylor series. It will give you the right solution. Alternatively, you can try to reduce the 2nd order ODE to a system of 1st order ODEs. But anyway, the Taylor series seems to be an always viable approach.