Let a < b, A and B be constants. Gâteaux differential of the functional ·b [* dx (y² +w²y² + 2yx¹), y(a)=A, y(b) = B, a S[y] = d. where w is a positive constant. Using the Gateaux differential show that the stationary path of S[y] satisfies the Euler-Lagrange equation,

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