Vidsemester test Remaining Time 00:43: Consider the variable coefficient linear homogeneous ODE a(z)y" + b(z)y' + c()y O
Posted: Thu May 12, 2022 12:39 pm
- Vidsemester Test Remaining Time 00 43 Consider The Variable Coefficient Linear Homogeneous Ode A Z Y B Z Y C Y O 1 (150.56 KiB) Viewed 28 times
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Vidsemester test Remaining Time 00:43: Consider the variable coefficient linear homogeneous ODE a(z)y" + b(z)y' + c()y O where 22 cos(I) a(I) =I, b() c(I) COS(1) + sin(1) ICOS(1) cos(+) + sin(1) A solution of the equation is y1 = cos(1) A second linearly independent solution can be found using reduction of order y2 = uyi where u(I) is an unknown function. The solution method involves solving a first order ODE for w(1) which determines the unknown function u(I) by solving another first order ODE w(I) = u() Which of the following is the expression for ud? ( I COS(1) COS(:)+sin() 2 sin () cos(x)) » COS) ICOS(:) COS(1)+sin() sin() +2 COS(1) TC05(1) cos(2)+sin() + ( + 2 sin(a) cos(z)) » w 0 ICOS(2) cos(-) +sin() sin(3) 2 w