Question

This is the whole question. For a) I put up the Euler Lagrange Equation and solved it, but for b) we also get boundary conditions. So, I tried to find C1 and C2, but I must have done something wrong as I.

Find the stationary functions for the following functionals:
(a) J[y] = ∫[x₁]^[x₂] (x(y')² - y(x)y'(x) + y(x)) dx
(b) J[y] = ∫[0]"

Answer 1

To find the stationary functions for the given functionals, we need to use the Euler-Lagrange equation. In part (a), we solve the Euler-Lagrange equation for the functional J[y] = ∫[x₁]^[x₂] (x(y')² - y(x)y'(x) + y(x)) dx. In part (b), we also consider boundary conditions.

Step-by-step explanation:

To find the stationary functions for the given functionals, we need to use the Euler-Lagrange equation. In part (a), we need to solve the Euler-Lagrange equation for the functional J[y] = ∫[x₁]^[x₂] (x(y')² - y(x)y'(x) + y(x)) dx. This will give us the stationary function. In part (b), besides solving the Euler-Lagrange equation, we also have boundary conditions to consider. You mentioned that you tried to find C1 and C2, but it seems that you made a mistake. Could you please provide your solution so that I can help you find the error?