Question: Euler Lagrange Equation VLy] = OL d OL Equation (3.11) ay - (x, y, y' ) - (x, y, y' ) = 0 dx dy'

Euler Lagrange Equation VLy] = OL d OL Equation (3.11) ay

Euler Lagrange Equation VLy] = OL d OL Equation (3.11) ay - (x, y, y' ) - (x, y, y' ) = 0 dx dy' Which is a second order ordinary differential equation, called the EulerLagrange equation, named after Leonhard Euler and Joseph-Louis Lagrange, two of the most important contributors to the calculus of variations. Equation (3.11) can be rewritten as: OL a2 L a2 L Ize E = day axdy' y dydy' a (y' ) 2 = 0 Question: If L independent of x and y: Then OL ax = 0 and OL -= 0. Please show the steps that ay Equation (3.11) becomes: y' = C1. Integrating again gives: y = Cix + C2

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