How Did Emmy Noether Derive Her Equation for Variational Symmetries in 1915?

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Noether's 1915 paper on variational symmetries reveals how to reformulate the Euler-Lagrange Equation using infinitesimals X and Y, allowing for a more efficient approach to solving differential equations. The discussion highlights the significance of symmetry as a powerful tool in mathematics and physics, encouraging young math majors to explore schools that offer courses in symmetry classes. Additionally, Leon Lederman's book, "Symmetry and the Beautiful Universe," is recommended as an accessible tribute to Noether's contributions. The original paper was located by the user, concluding the search for it. Understanding Noether's work is essential for advancing in the field of differential equations.
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I am in need of Noether's paper she wrote in around 1915 about variational symmetries.

I need to know how she found that [for an ode L(x,y,y')]if an X and Y (infinitesimals) exists then you can rewrite the Euler-Lagrange Equation in terms of L(x,y,y'), X(x,y) and Y(x,y).

This is really amazing how she didn't this. So instead of solving for y(x) in the E-L equ you can just plug it into the equation she came up with.

If anyone could find the paper she wrote that would be awesome!

Thanks
 
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Ok, I found it. thanks anyways.(http://www.physics.ucla.edu/~cwp/lists/accDB_su.html)

Symmetry is THE most powerful tool in solving differential equations. If you are a young math major you should difinitely think about going to a school where symmetry classes are avaliable.
 
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Speaking of Emmy Noether...

Leon Lederman has written an excellent, non-technical book dedicated to symmetry in physics. It is a long-overdue, popular homage to Emmy Noether!

Symmetry and the Beautiful Universe
by Leon M. Lederman & Christopher T. Hill​
 
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