A1. Solve the Euler-Lagrange equation for the following functionals: (b)* f [y + xy'] dx (e)*...

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A1. Solve the Euler-Lagrange equation for the following functionals: (b)* f [y + xy'] dx (e)* f [(1 + x) (y')] dx (c) fx [12xy + (y')] dx 20 (f)* f [y' (1 + xy')] dx x0 You DO NOT need to apply the boundary conditions. A1. Solve the Euler-Lagrange equation for the following functionals: (b)* f [y + xy'] dx (e)* f [(1 + x) (y')] dx (c) fx [12xy + (y')] dx 20 (f)* f [y' (1 + xy')] dx x0 You DO NOT need to apply the boundary conditions.