One of the following pairs of functions are linearly dependent on (0, 0) f(x) = el-3r, 8(x) = e6-Ir f(x) = x, g(x) = r? f (x) = e²-3r, 8 (x) = O f(x) = 2, g(xr) = 2r

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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One of the following pairs of
functions are linearly dependent on (0, o0)
f(x) = el-3r,
%3D
8(x) = e6-3
f(x) = x,
g(x) = r
%3D
f (x) = e2-3r,
8 (x) = e*
f(x) = 2, g(x) = 2r
f(x) = e cos(r),
%3D
g(x) = e sin(x)
f(x) = e.
g(x) =
%3D
%3D
Transcribed Image Text:One of the following pairs of functions are linearly dependent on (0, o0) f(x) = el-3r, %3D 8(x) = e6-3 f(x) = x, g(x) = r %3D f (x) = e2-3r, 8 (x) = e* f(x) = 2, g(x) = 2r f(x) = e cos(r), %3D g(x) = e sin(x) f(x) = e. g(x) = %3D %3D
Find the least order for homogenous
D. E. with constant coefficient
which has the solution :
6.x + 9.xe
y(x)
cos(2r)
%3D
Transcribed Image Text:Find the least order for homogenous D. E. with constant coefficient which has the solution : 6.x + 9.xe y(x) cos(2r) %3D
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