- #1
squelch
Gold Member
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Homework Statement
For each of the following, determine if the system is linear. If not, clearly state why not.
(a) ##y''(t)+15y'(t)+sin(y(t)))=u(t)##
(b) ##y''(t)-y'(t)+3y(t)=u'(t)+u(t)##
(c) ##y'(t)=u(t)## and ##z'(t)=u(t)-z(t)-y(t)##
Homework Equations
None
The Attempt at a Solution
Intuitively, I believe that the ##sin(y(t))## term makes (a) nonlinear, while all of the others can be expressed as linear differential equations, but I wasn't sure. I was hoping for a bit of a sanity check on this. Does the introduction of a trigonmetric function like sin() make these nonlinear all of the time, or is it just that the function is nested, e.g. as ##sin(y(t))##?