Extremise the functional: $$ J[y]=\int_0^1 (yy')^2 dx$$ subject to the constraint $$ \int_0^1 y^2 dx=3, $$ And the boundary conditions $y(0)=1$ and $y(1)=2$.
2026-04-10 11:37:11.1775821031
Extremising a functional with conditions
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