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 $y(1)=2$.
Extremising a functional with conditions
1
$\begingroup$
calculus
calculus-of-variations
-
0What have you tried? Could you form a precise question instead of just stating a problem from a book or homework? – 2012-11-25
-
0I 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 usefull – 2012-11-25