Using Euler's equation for \(y(x)\), prove that

This equation provides an alternative method for solving problems in which the integrand \(f\) is not an explicit function of \(x\), because in that case the quantity \(f-y^{\prime} \partial f / \partial y^{\prime}\) is constant, which is only a first-order differential equation.

Transcribed Image Text:

af d of = 0. dx