general solution of euler equation

[craig11]

Find the general solution of the Euler equation corresponding to the functional g(y) = integ(a to b) f(x) sqrt(1+ y' ^2) dx and investigate the special case f(x) = sqrt (x)

I need to know how to do this for a test.
I think what's throwing me off is the integral, g(y) = ..., and i don't recall finding the general solution in class so i'm not sure what procedures i take to do this.

 

[royhaas]

Look at the Euler-Lagrange equation when the integrand is constant with respect to y.

 

[craig11]

i'm not quite sure which equation you are talking about, is it this one?
F- y' F(small y') = C, i found this equation for an example where the equation is : integral(x0 to x1) y sqrt(1+y'^2)) dx, is this the same integral except f(x) is written as y?

 

[craig11]

nevermind i got this, thanks!