Consider the functional J[y]=inta^bF(x,y,y')dx where F(x,y,y')=1+y^2/y'^2 for admissible function y(x). Which of the following are extremals for J?

(C) y(x)=sinh(Ax+B) where A, B are constants

Q84Section II (Mathematics)84 of 190

Beltrami's identity for an $x$ -free integrand gives a hyperbolic-sine family

Consider the functional $J[y]=\int_a^bF(x,y,y')dx$ where $F(x,y,y')=\dfrac{1+y^2}{y'^2}$ for admissible function $y(x)$ . Which of the following are extremals for J?

Pick an option to check your answer.

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