Solving the differential equation y''=a√(1+(y')²) for a catenary

[becksftw]

(Moderator's note: thread moved from "Differential Equations")

The DE is y''=a*sqrt(1+(y')^2)

I have no idea how to go about integrating it, I just started taking diff eq's and haven't taken calc in over a year. Any help would be appreciated, thanks!

 

[torquil]

The DE is y''=a*sqrt(1+(y')^2)

I have no idea how to go about integrating it, I just started taking diff eq's and haven't taken calc in over a year. Any help would be appreciated, thanks!

A first step could be to define a new function u := y'

Then rewrite:

u'/sqrt(1+u^2) = a

and then integrate both sides with respect to time or space or whatever variable y depended on.

Torquil