Question: Please show all steps! Thanking you in advance! Question 2 - 20 marks (a) Find the two coupled Euler-Lagrange equations giving the stationary path of

Please show all steps! Thanking you in advance!

Question 2 - 20 marks (a) Find the two coupled Euler-Lagrange equations giving the stationary path of the functional Sly1, y2] = dac [y? + 292 + (2y1 + 92)?]. (b) By making the linear transformation 21 = y1 + ay2, z2 = 2y1 + y2 to the new dependent variables (z1, z2), where a is a constant, find the value of a such that the functional can be written as the sum of two functionals, one of which depends only on z1 and the other only on z2. (c) Find the general solution of the Euler-Lagrange equations for (21, Z2), and hence find the general solution for (y1, y2). (d) Verify by direct substitution that your general solution for (y1, y2) satisfies the Euler-Lagrange equations found in part (a)

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