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Let Aly) be a smooth function and letJ(y) = J" A6)y' &xandIy) =Vi+y2 dr_Formulate the Euler-Lagrange equations for the isoperimetric problem with y(0...

Question

Let Aly) be a smooth function and letJ(y) = J" A6)y' &xandIy) =Vi+y2 dr_Formulate the Euler-Lagrange equations for the isoperimetric problem with y(0) 0, 9(1) = 1, and I(y) = L > V2. Show that A = 0, and that there are an infinite number of solutions to the problem. Explain without using the Euler-Lagrange equations (or any conservation laws) why there must be an infinite number of solutions to this problem:

Let Aly) be a smooth function and let J(y) = J" A6)y' &x and Iy) = Vi+y2 dr_ Formulate the Euler-Lagrange equations for the isoperimetric problem with y(0) 0, 9(1) = 1, and I(y) = L > V2. Show that A = 0, and that there are an infinite number of solutions to the problem. Explain without using the Euler-Lagrange equations (or any conservation laws) why there must be an infinite number of solutions to this problem:

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