(4) Find the extremal of the functional (i.e. the curve y(x) which gives a stationary value)...

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(4) Find the extremal of the functional (i.e. the curve y(x) which gives a stationary value) of x2 I = = [ [y(1 + xy')] dx 1 subject to the fixed boundary condition at x = x of y(x1) = y and the natural boundary condition at x = x2. (5) Find the curve y(x) that minimizes the integral = [{}{() + : (y' ) + yy' + y' + : + y] dr I = 0 when the values of y(0) and y(1) are not specified. (4) Find the extremal of the functional (i.e. the curve y(x) which gives a stationary value) of x2 I = = [ [y(1 + xy')] dx 1 subject to the fixed boundary condition at x = x of y(x1) = y and the natural boundary condition at x = x2. (5) Find the curve y(x) that minimizes the integral = [{}{() + : (y' ) + yy' + y' + : + y] dr I = 0 when the values of y(0) and y(1) are not specified.