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Q85Section II (Mathematics)85 of 180

Euler equations for a two-variable parametric functional, combined into a 4th-order ODE

The Euler's equation for the extremization of the functional I(y(x))=∫0π/2(2xy+x′2+y′2)dt,x′=dx/dtI(y(x))=\int_0^{\pi/2}(2xy+x'^2+y'^2)dt, x'=dx/dt, is:

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