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3 Consider the equation + ax + bx = 0 when b = a², so that the characteristic equation has a double solution m = -a. Suppose that the differential equation has a solution of the form x(t) = u(t)emt. Prove that this is a solution if and only if ü = 0. Conclude that the general solution is x = (A + Bt)e-at/2. (Here * = d and = d.)

3 Consider the equation + ax + bx = 0 when b = a², so that the characteristic equation has a double solution m = -a. Suppose that the differential equation has a solution of the form x(t) = u(t)emt. Prove that this is a solution if and only if ü = 0. Conclude that the general solution is x = (A + Bt)e-at/2. (Here * = d and = d.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3 Consider the equation ï + ax + bx = 0 when b = a², so that the characteristic equation has a double solution m = =-a. Suppose that the differential equation has a solution of the form x(t) = u(t)emt. Prove that this is a solution if and only if ü = 0. Conclude that the general solution is x = de and x = da.) (Here i = (A + Bt)e-at/2
Transcribed Image Text:3 Consider the equation ï + ax + bx = 0 when b = a², so that the characteristic equation has a double solution m = =-a. Suppose that the differential equation has a solution of the form x(t) = u(t)emt. Prove that this is a solution if and only if ü = 0. Conclude that the general solution is x = de and x = da.) (Here i = (A + Bt)e-at/2
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