Non-order DE

Dec 2015
1,084
169
Earth
\(\displaystyle Y'' e^{Y''}=x\)
 

romsek

Math Team
Sep 2015
2,964
1,674
USA
crazily enough it has a closed form answer

$y(x)=c_2 x+c_1+\dfrac{x^2 \left(4 W(x)^3-6 W(x)^2+6 W(x)+1\right)}{8 W(x)^2}$

where $W(x)$ is Lambert's $W$ function

Where do you come up with these questions?
 
  • Like
Reactions: 2 people