Problem 6. (10 points) (1) (4 pts) Determine whether the following problems are initial-value or boundary-value problems

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Problem 6 10 Points 1 4 Pts Determine Whether The Following Problems Are Initial Value Or Boundary Value Problems 1 (42.44 KiB) Viewed 12 times

Problem 6. (10 points) (1) (4 pts) Determine whether the following problems are initial-value or boundary-value problems: daw d'w dr B; wo)- w(L) = 0; d?w (1)-0. (a). -- dx² dr (b). y" + 2y = 0; y(O) = 0; y(1) = 0. (c). y" + sin(x)y' + cos(x)y=0; y(O)= 1, y'(0) = 0. (d). y" + y = 0; y(0) + y'(0) = 0, y(1) = 0. d'w - iw = 0; dx dx w (0)- "()- w(1)- dw(1)-0. - dw W = (e). dr (2) (6 pts) The equation of motion of a simple pendulum, subject to damping and external torque M (1), is given by do de m/ + c dt + mgl sin(0)-M, (1) dt? where m, l, c, g are constants. Express this equation as a system of linear first-order equations.