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March 21st, 2018, 08:21 AM  #1 
Senior Member Joined: Dec 2015 From: somewhere Posts: 536 Thanks: 81  Nonorder DE
$\displaystyle Y'' e^{Y''}=x$

March 21st, 2018, 08:41 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,458 Thanks: 1340 
crazily enough it has a closed form answer $y(x)=c_2 x+c_1+\dfrac{x^2 \left(4 W(x)^36 W(x)^2+6 W(x)+1\right)}{8 W(x)^2}$ where $W(x)$ is Lambert's $W$ function Where do you come up with these questions? 

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