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Q84Section II (Mathematics)84 of 190

Solving a boundary value problem from Euler–Lagrange

An extremum of the functional ∫01(y′2−12xy)dx,y(0)=0, y(1)=1\int_0^1(y'^2-12xy)dx, y(0)=0,\ y(1)=1 can occur only along the curve:

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