Question: Find the Euler-Lagrange equations for the following functional, assuming that y(x) is fixed at the boundaries and g(x) and p(x) are sufficiently smooth that

Find the Euler-Lagrange equations for the following functional, assuming that y(x) is

Find the Euler-Lagrange equations for the following functional, assuming that y(x) is fixed at the boundaries and g(x) and p(x) are sufficiently smooth that all the necessary operations are kosher: J[y] = [p(x) (Vy Vy) + q(x)y(x)] dx.

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