Let x = x(t) be a twice-differentiable function and consider the second order differential equation x" + ax' + bx = 0 (11) %3D (a) Show that the change of variables y = x' and z = x allows Equation (11) to be written as a sys- tem of two linear differential equations in y and z.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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I want an answer of question number 69.

as u have told u can only answer 3 subparts.

i want an answer of only a, and b sub part.

Let x = x(t) be a twice-differentiable function and
consider the second order differential equation
x" + ax' + bx = 0
(11)
%3D
(a) Show that the change of variables y = x' and
z = x allows Equation (11) to be written as a sys-
tem of two linear differential equations in y and z.
Transcribed Image Text:Let x = x(t) be a twice-differentiable function and consider the second order differential equation x" + ax' + bx = 0 (11) %3D (a) Show that the change of variables y = x' and z = x allows Equation (11) to be written as a sys- tem of two linear differential equations in y and z.
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