Consider the variable coefficient linear homogeneous ODE a(x)y" +b(x)y' + c(x)y=0 where 1+6 In(x) a(x) = x-1, 6(x) = 22

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Consider The Variable Coefficient Linear Homogeneous Ode A X Y B X Y C X Y 0 Where 1 6 In X A X X 1 6 X 22 1 (97.42 KiB) Viewed 22 times

Consider the variable coefficient linear homogeneous ODE a(x)y" +b(x)y' + c(x)y=0 where 1+6 In(x) a(x) = x-1, 6(x) = 22 (2 In(x) +1) c() = -4 23 (2 ln(2) +1) A solution of the equation is yu = ln(2). A second linearly independent solution can be found using reduction of order y2 = Uy1 where u(x) is an unknown function. The solution method involves solving a first order ODE for w(x) which determines the unknown function u(x) by solving another first order ODE w(x) = u(x). Which of the following is the expression for w' ? 1+6 In() 2x ln() + 2 tr) < ln(2) 1+6 In(2) 2 x ln(x)+ In(2) +2 ) w I 1+6 In(2) 2x In()+x +2 w In(3) O ( 1+6 In() 2 x ln(x) + In(a) 2 ) w W 1