A third order linear, homogeneous DE whose general solution is y(t) = C₁e-2t + C₂e-t + Cet is: [Hint: The general solution implies that r=-2,-1 and 1 are the roots of the characteristic equation. Hence r+2, r+1 and r-1 are the factors of the characteristic equation.] OA none of these OB.y"" + 2y"+y' + 2y = 0 Ocy"" + 2y" -y' + 2y = 0 OD.y" - 2y"+y' + 2y = 0 OEy"" + 2y" - y' - 2y = 0
A third order linear, homogeneous DE whose general solution is y(t) = C₁e-2t + C₂e-t + Cet is: [Hint: The general solution implies that r=-2,-1 and 1 are the roots of the characteristic equation. Hence r+2, r+1 and r-1 are the factors of the characteristic equation.] OA none of these OB.y"" + 2y"+y' + 2y = 0 Ocy"" + 2y" -y' + 2y = 0 OD.y" - 2y"+y' + 2y = 0 OEy"" + 2y" - y' - 2y = 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![A third order linear, homogeneous DE whose general solution is
y(t) = C₁e-²t + C₂e-t + Сzet
is:
[Hint: The general solution implies that r=-2,-1 and 1 are the roots of the characteristic
equation. Hence r+2, r+1 and r-1 are the factors of the characteristic equation.]
O A none of these
O B. y'" + 2y"+y' + 2y = 0
Ocy"" + 2y" - y' + 2y = 0
O D.y"" - 2y"+y' + 2y = 0
O Ey"" + 2y" - y' - 2y = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06089eb2-ff0d-4c09-8152-ab59813eefd5%2F90c8a029-f3bf-4b1e-9ea3-16409f5eb0e1%2Fz0zknrt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A third order linear, homogeneous DE whose general solution is
y(t) = C₁e-²t + C₂e-t + Сzet
is:
[Hint: The general solution implies that r=-2,-1 and 1 are the roots of the characteristic
equation. Hence r+2, r+1 and r-1 are the factors of the characteristic equation.]
O A none of these
O B. y'" + 2y"+y' + 2y = 0
Ocy"" + 2y" - y' + 2y = 0
O D.y"" - 2y"+y' + 2y = 0
O Ey"" + 2y" - y' - 2y = 0
Transcribed Image Text:Solving the DE
dx t+x
dt
t
=
t> 0
with the homogeneous method yields
x(t) = lnt + Ct,
where C is an arbitrary constant.
True
O False
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