Question: Using the Euler-Lagrange Equation, find the general functional form of the path y(x) that extremizes the functional . S2 Jly] = Vids , (1) JS1

Using the Euler-Lagrange Equation, find the general functional form of the

Using the Euler-Lagrange Equation, find the general functional form of the path y(x) that extremizes the functional . S2 Jly] = Vids , (1) JS1 where ds = vdx2 + dy? is the length of a short segment on the path y(x) that connects the points S1 = (x1, y1) and S2 = (12, y2). [ You don't need to substitute the specific boundary conditions; leaving the answer in terms of general integration constants is fine

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