Consider the variable coefficient linear non-homogeneous ODE a(Q)y" + b(e)y' + c()y=d(x) where a(z) = (ln(x))-1, b() = s

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Consider The Variable Coefficient Linear Non Homogeneous Ode A Q Y B E Y C Y D X Where A Z Ln X 1 B S 1 (120.16 KiB) Viewed 30 times

Consider the variable coefficient linear non-homogeneous ODE a(Q)y" + b(e)y' + c()y=d(x) where a(z) = (ln(x))-1, b() = sin(x) (In(x)22 - 1) In(2)x (cos(x) ln(2)x – sin(x)) and c(a) sin(2)x - cos(x) In(x)x(cos() In(x)2 + sin(x)) d(z) = - cos(2) In(2x+ sin(x) In(2). The two linearly independent solutions of the associated homogeneous equation are yu = sin(x), y2 = ln(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? O-sin() 0 - In(2) O sin(3) In() (b) Which of the following is the expression for v'? In(3) O sin(2) - sin(x) 0 - In(2)