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Construct the Lagrangian and Compute the Noether symmetries, first integrals of the combined gravity inertial rossby wave equation + g(x)y = 0, where g(x)

Construct the Lagrangian and Compute the Noether symmetries, first integrals of the combined gravity inertial rossby wave equation + g(x)y = 0, where g(x) is an arbitrary function of x. dx?

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