Suppose y(x) is the extremal of the variational problem J(y)=int0^1x^2(y')^2,dx subject to y(0)=0, y(1)=1, int0^1y^2,dx=frac17. Then which of the following statements are true?

Q98Section C (Part C)98 of 120

Calculus of variations — an isoperimetric constraint

Suppose $y(x)$ is the extremal of the variational problem $J(y)=\int_0^1x^2(y')^2\,\mathrm{d}x$ subject to $y(0)=0$ , $y(1)=1$ , $\int_0^1y^2\,\mathrm{d}x=\frac17$ . Then which of the following statements are true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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