The solution of the system of the equation 5 x + 3 y = 11 and 2 x − 7 y = 16 with elimination method

Question

Q2*) Consider the extremisation of the integral I[y] = √²² F(x,y,y', y") dx x1 when y and y' are prescribed only at x = x1. Derive the so-called 'natural boundary conditions' that must be satisfied at x = x2. Taking a specific example: The functional I [y] is defined by I[y] = √² ((y″)² + y) dx with y(0) = 0 and y'(0) = 0. Write down the fourth-order Euler-Lagrange equation for this problem, stating the four boundary conditions. Find the general solution of the Euler-Lagrange equation, and then impose the boundary conditions to find the extremal.

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Chapter 11.0B, Problem 20E

To determine

To find:

The solution of the system of the equation 5x+3y=11 and 2x−7y=16 with elimination method

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