2x= y+e *t %3D 3y eSt

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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Question
Let D -D
be the differential operators. When determinant
method is applied to the system of differential equations
dx
2x- y+e ",
dt
dy
X3y e st
dt
which of the following is the value of the determinant of eoefficient matrix of
the system?
a) D2 + 2D = 3
b) D² + 3D = 2
c) D2 -D+1
d) D2 + D-2
e) D2 + D - 5
Transcribed Image Text:Let D -D be the differential operators. When determinant method is applied to the system of differential equations dx 2x- y+e ", dt dy X3y e st dt which of the following is the value of the determinant of eoefficient matrix of the system? a) D2 + 2D = 3 b) D² + 3D = 2 c) D2 -D+1 d) D2 + D-2 e) D2 + D - 5
Consider the system of differential equations
dx
-3x +y,
dt
dy
-5x + 3y + 3sint
dt
which of the following is the complementary(homogeneous) solution of x(t)?
a) x,(() = Get + ze
b) x,(() = ge?t + c,e ?"
c) x,(t) = qe' + c,e 2"
d) x,(() = ,et + c,e 2#
e) x,(() = ge' + cC,te
Transcribed Image Text:Consider the system of differential equations dx -3x +y, dt dy -5x + 3y + 3sint dt which of the following is the complementary(homogeneous) solution of x(t)? a) x,(() = Get + ze b) x,(() = ge?t + c,e ?" c) x,(t) = qe' + c,e 2" d) x,(() = ,et + c,e 2# e) x,(() = ge' + cC,te
Expert Solution
Step 1

In these questions, we have to find the determinant for the system of the differential equations.

dxdt=2x-y+e-4tdydt=x-3y-e-5t

 

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