14.5 Problems 1. Determine the Green's function for y"(x) + y(x) = f(x) with the boundary conditions y(0)=0 and y'(1)=0. 2. Use the Green's function in Problem 1 to solve y"(x) + y(x)=x with the boundary conditions y(0)=0 and y(1)=0. & Determine the Green's function for y" (x) + y(x) = f(x) with the boundary conditions y'(0) = 0 and y'(1)=0. 4. Use the Green's function in Problem 3 to solve the equation y"(x) + y(x)=x with the boundary conditions y(0)=0 and y'(1) = 0. 5 Solve the Green's function for the equation G (x, z) + G(x, z) = -8(x − 2) with the boundary conditions G(0,2)=0 and G'(1, z) = 0. Solve the Green's function for the equation G" (x, z) + G(x, z) = -8(x − 2) with the boundary conditions G(0,2)=0 and G'(1, 2) = 0. 1. Use the Green's function in Problem 5 to solve the equation y"(x) + y(x)=x with the boundary conditions y(0)=0 and y'(1) = 0. & Use the Green's function in Problem 6 to solve the equation y"(x) + y(x)=x with the boundary conditions y'(0)=0 and y'(1)= 0. 9. Use the method of undetermined coefficients to solve the equation y"(x)+ y(x)=x subject to the boundary conditions y(0)=y(1) = 0. Compare your result to the one that you obtained in Example 3. 10. Use the method of variation of parameters to re-do Problem 9. 11. Use the method of undetermined coefficients to solve the equation y"(x) + y(x)=x subject to the boundary conditions y(0) = 0 and y' (1) = 0. Compare your answer to the one that you obtained in Problem 7. 12. 11.