The extremal of the functional
y(0) = 0, y(1) = 1, y ∈ C²[0, 1] is

Question

Question

This question was previously asked in

CSIR-UGC (NET) Mathematical Science: Held on (26 Nov 2020)

Answer 1

Concept: If then its extremum is

Explanation:

y(0)=0, y(1) = 1,

According to the question

= 0

⇒ = 0

⇒ x - 4y'' = 0

after integrating with respect to x, we get

again integrating with respect to x, we get

where c and d are constants of integration

now,

and

Hence our extremum would be

Hence option (4) is correct

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