Which man came up with the solution to the basic Calculus of Variations problem first?

http://en.wikipedia.org/wiki/Euler-Lagrange

Makes it sound like Lagrange got it first in 1755, then sent it to Euler.

But

http://en.wikipedia.org/wiki/Calculus_of_variations

makes it sound like Euler got it in the 1730s.

Could somebody please explain which man actually wrote out the equation first, and what the other then contributed to it?