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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 $y(1)=2$.

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    What have you tried? Could you form a precise question instead of just stating a problem from a book or homework?2012-11-25
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    I have tried forming $H=(yy')^2+\lambda y^2$ and tried to find the Euler-Lagrange equation of this. However I don't find any answers that are usefull2012-11-25

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