Consider the following fifth-order linear homogeneous initial value problem with constant coefficients: y (5) +y (4)-y¹ - y=0, y (0)=y '(0)=y" (0) =y (3) (0) =y (4) (0) = 0 Choose all correct answers (A) The roots of the characteristics equation are: 1, -1, -1, i, -i A general solution is given by B (D) y= A e + Bxe + Ce+D cos(x) + E sin(x) where A, B, C, D and E are contants. There exists a non-trivial solution of the given initial value problem where y (x) #0 for some values of x. A general solution is given by -X y= A e + Be + C xe¯*+D cos(x) + E sin(x) where A, B, C, D and E are contants. E The roots of the characteristics equation are: 1, 1, -1, i, -i F The only solution of the given initial value problem is the trivial solution, y = 0.
Consider the following fifth-order linear homogeneous initial value problem with constant coefficients: y (5) +y (4)-y¹ - y=0, y (0)=y '(0)=y" (0) =y (3) (0) =y (4) (0) = 0 Choose all correct answers (A) The roots of the characteristics equation are: 1, -1, -1, i, -i A general solution is given by B (D) y= A e + Bxe + Ce+D cos(x) + E sin(x) where A, B, C, D and E are contants. There exists a non-trivial solution of the given initial value problem where y (x) #0 for some values of x. A general solution is given by -X y= A e + Be + C xe¯*+D cos(x) + E sin(x) where A, B, C, D and E are contants. E The roots of the characteristics equation are: 1, 1, -1, i, -i F The only solution of the given initial value problem is the trivial solution, y = 0.
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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Transcribed Image Text:Consider the following fifth-order linear homogeneous initial value problem with constant coefficients:
y (5) +y (4)-y¹ - y=0,
y (0)=y '(0)=y" (0) =y (3) (0) =y (4) (0) = 0
Choose all correct answers
(A) The roots of the characteristics equation are: 1, -1, -1, i, -i
A general solution is given by
B
(D)
y= A e + Bxe + Ce+D cos(x) + E sin(x)
where A, B, C, D and E are contants.
There exists a non-trivial solution of the given initial value problem where
y (x) #0 for some values of x.
A general solution is given by
-X
y= A e + Be + C xe¯*+D cos(x) + E sin(x)
where A, B, C, D and E are contants.
E The roots of the characteristics equation are: 1, 1, -1, i, -i
F The only solution of the given initial value problem is the trivial solution, y = 0.
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