For each of the ODEs in the 1st column, indicate whether it is: 1. linear time-invariant (LTI), linear time-varying (LTV), or nonlinear 2. 1st order, 2nd order, or higher order 3. homogeneous or inhomogeneous (only for the case of linear systems-for nonlinear sys- tems you can leave the last column blank) by marking the appropriate column. The unknown function x(t) represents the state of some mechanical system and t represents time. Hint: An ODE is considered nonlinear only if the nonlinearity involves the unknown function x(t). System ODE * + 3tx = 0 (x-x)²+1=0 t²x+bx+cx=0 x = 0 x + x + x-2= * + sin(x) = 0 etx+ x = sint x + x = 0 xx+a+bt = 0 x-bx² = 0 Linearity? Order? LTI LTV NL 1st 2nd Higher Homog. Inhomog. Homogeneity?
For each of the ODEs in the 1st column, indicate whether it is: 1. linear time-invariant (LTI), linear time-varying (LTV), or nonlinear 2. 1st order, 2nd order, or higher order 3. homogeneous or inhomogeneous (only for the case of linear systems-for nonlinear sys- tems you can leave the last column blank) by marking the appropriate column. The unknown function x(t) represents the state of some mechanical system and t represents time. Hint: An ODE is considered nonlinear only if the nonlinearity involves the unknown function x(t). System ODE * + 3tx = 0 (x-x)²+1=0 t²x+bx+cx=0 x = 0 x + x + x-2= * + sin(x) = 0 etx+ x = sint x + x = 0 xx+a+bt = 0 x-bx² = 0 Linearity? Order? LTI LTV NL 1st 2nd Higher Homog. Inhomog. Homogeneity?
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:For each of the ODEs in the 1st column, indicate whether it is:
1. linear time-invariant (LTI), linear time-varying (LTV), or nonlinear
2. 1st order, 2nd order, or higher order
3. homogeneous or inhomogeneous (only for the case of linear systems-for nonlinear sys-
tems you can leave the last column blank)
by marking the appropriate column. The unknown function x(t) represents the state of some
mechanical system and t represents time. Hint: An ODE is considered nonlinear only if the
nonlinearity involves the unknown function x(t).
System ODE
x + 3tx = 0
(x − x)² + 1 = 0
t²x+bx+cx = 0
x = 0
x+x+x - 2 =
* + sin(x) = 0
etx + x = sint
x + x = 0
xx+a+bt = 0
xbx² = 0
Linearity?
Order?
LTI LTV NL 1st 2nd Higher Homog. Inhomog.
Homogeneity?
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