Let n I be a positive integer. Show that the functional •1 S[y] = √² dx (y')"e", y(0) = 1, y(1) = A > 1, has a stationary path given by y = = eA/n - e¹/n. C= n ln(cx + e¹/n), where

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A: If , then to determine the meaning of .

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A: y' = dy/dx y(6) = 5 means at x=6 => y=5

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A: To show that the given identity is true,

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A: Given system of inhomogeneous linear equations is given below:  3x-2y+z=0  -2x+7y+z=21  x+3y-4z=19…

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A: We use chain rule

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A: This question is based on Quotient rule of differentiation.

Q: Find y as a function of if y(0) = 2, y'(0) = 9, y'(0) = -58. y(x) = y"-4"-y + 4y = 0,

A: We are given the homogeneous differential equation: y"'-4y"-y'+4y=0 and y(0)=2, y'(0)=9,y"(0)= -58.