Answer Happy

Consider the variable coefficient linear non-homogeneous ODE a(z)y" + b(r)y' + c(I)y=d(2) + where a(z) ==-1, b(I) = COS(2) cos(2) + sin() and 1 (2) = cos(2) I (cos(I) + sin(t)) d) I cos(2) The two linearly independent solutions of the associated homogeneous equation are 91 = cos(I), y2 = 2 A particular solution to the non-homogeneous equation can be found using the method of variation of parameters, yp = uyi + vy2 where u and v are unknown functions. The solution method involves solving two first order ODEs for u and v. (a) Which of the following is the expression for u? COS(I)(cos(1)+sin(I):) (cos(2)+sin(x).)-1 O-(cos(T) + sin(2))-1 cos(z)(cos(x)+sin(x2) (b) Which of the following is the expression for v' ? (cos(I) + sin(2))-1 T cos(z) (cos(x)+sin(2x) O -(cos(x)+sin(x).)-1 cos()(cos(1)+sin(t))