Mi e forlogeneous eq for problems 11-20, carry out the following steps. (a) verify that the functions y, and y, are solutions of the specified differential equation. (b) verify that y, and y, are linearly independent. (c) find the general solution of the differential equation. (d) find the solution of the indicated initial-value problem. 11 y" = 0 y.(x) = 1 yz(x) = x 12. y" – 5y' + 6y = 0 y(0) = 0 y'(0) = 1 y(x) = 24 y(0) = 0 y'(0) = 0 13. y" + 5y' + 6y = 0 yı(x) = e-2 y(o) = 0 y'(0) = 1 14. y" – 4y = 0 y(0) = 1 y(0) = 1 15. y" - 5y = 0 y(0) = 1 y'(0) = 0 16. y + 4y = 0 yı(x) = sin 2x ya(x) = cos 2x y(o) = 1 y'(0) = 1 17. y" - y = 0 (2) = sinh x y2(x) = coshx y(0) = 0 y'(o) = 1 18. y" - 2y + y = 0 yı(x) = et v2(x) = xe".. (o) = 1 y'o = 1 19. ry" + xy' - y = 0 y.(x) = x y(1) = 0 y'(1) = 0 y(x) = x y(1) = 1 20. x y" – 2y = 0 y'(1) = 1 yı(x) = 2 yı(x) = e y2(x) = el y2(x) = -34 ya(x) = e-2 yz(x) = e-vs = yz(x) = x-1 yı(x) = x