If the characteristic equation of a second-order constant coefficient homogeneous linear differential equation has roots m1> 0 and -m2 <0, the solution of the differential equation is x(t) = Ae^(m1t) + Be^(m2i) and initial conditions are usually x(0) an x'(0) = b0. In this case it will be x(t) → Foo for t o, but in a special case x(t) → 0 can be obtained for t → 0. Find the relationship between a0 and b0 that satisfies this situation. %D a0 %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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If the characteristic equation of a
second-order constant coefficient
homogeneous linear differential
equation has roots m1> 0 and -m2 <0,
the solution of the differential equation
is x(t) = Ae^(m1t) + Be^(m21)
and initial conditions are usually x(0)
an x'(0) = b0.
In this case it will be x(t) → Fo for t →
o, but in a special case x(t) → 0 can be
obtained for t → 0.
%D
a0
%3D
Find the relationship between a0 and
b0 that satisfies this situation.
Transcribed Image Text:If the characteristic equation of a second-order constant coefficient homogeneous linear differential equation has roots m1> 0 and -m2 <0, the solution of the differential equation is x(t) = Ae^(m1t) + Be^(m21) and initial conditions are usually x(0) an x'(0) = b0. In this case it will be x(t) → Fo for t → o, but in a special case x(t) → 0 can be obtained for t → 0. %D a0 %3D Find the relationship between a0 and b0 that satisfies this situation.
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