Can someone help. This question is from my Classical Mechanics class. The topic is from Calculus of Variations and this problem involves the Euler Lagrange Equation.

Question

Can someone help.  This question is from my Classical Mechanics class.  The topic is from Calculus of Variations and this problem involves the Euler Lagrange Equation.

anonymous · Answer

Oka

anonymous · Answer

Find the equation of the path joining the origin O to the point P(1,1)  in the xy plane that makes the integral stationary.

$$\int\limits_{O}^{P} (y \prime ^2 +yy \prime +y^2) dx$$

anonymous · Answer

I got this far.  I need to find the function y(x) that will satisfy this condition.

$$y \prime \prime -y = 0$$

anonymous · Answer

the solution of that differential equation is Asin(x)+Bcos(x).... now depending on the boundary conditions u can get A and B...