Calculate and sketch the extremals of integral (from 1 to b) of (x^2*y'^2 + 12y^2) dx which pass through (1,1) and where b>1.
There is a hint, to solve the Euler-Lagrange equation, try solutions of the form y = x^p but I don't see how that helps.
Any help would be appreciated.
Well, what is the Euler-Lagrange equation for this problem?
(x^2)y'' + 2xy' -12y = 0
Thanks, so does that mean the coefficient of the first derivative is
? Not sure on this.
just wondering, did I get my ELeqn correct or is it meant to be 6y - xy' = 0 ? As I'm not sure if you're meant to differentiate both terms in d/dx ( 2x^2 * y') as y' is a function of x..?