Suppose y(x) is the extremal of the variational problem J(y) = ∫04 (y')2y2 dx subject to y(0) = 1, y(4) = e8. Which of the following statements is true?

Find the curve that extremizes the functional I(y) = ∫01 [(dydx)2 + 12xy] dx for the given boundary conditions y(0) = 0 and y(1) = 1.

For a, b, c ∈ ℝ, consider the variational problem: Minimize J[y] = ∫02 [a(y')2 + 2byy' + cy2] dx subject to y(0)=10, y(1)=100. Then which of the following statements is true?