Re: Linearity question, is the proffesor wrong ?

Gib wrote
I've taught a Mathematical Modelling course in the School of
Engineering. In this course we classify ODEs using the definition of
non-linear that you use, in other words it refers only to the way that y
and its derivatives appear in the equations. Another element of
classification is whether the coefficients are constant or functions of
t. The treatment is not mathematically advanced, being limited to
solving 2nd order systems by means of the characteristic equation, but
it may be at a similar level to the course you're teaching.'ve test


Hi all, the proffessor answered me and suggested me to perform a test,
which I did.
I've tested letting u(t)= unit step function as well as u(t)=2*unit
step function
The steady state value in the first test is 5, and in the second 7. It
should have been 10 according to linearity test.

I am confused now ....
Linearity definition is with respect to an operator, if a1 =D(b1) then
c*a1=D(c*b1), where c is a constant, and if a2=D(b2), then
a1+a2=D(b1+b2).

In the case of D.E. I should put in the solution y(t) into the
linearity definition.
y(t)=D(y(t)), c*y(t)=D(c*y(t)) etc.
With respect to this definition the D.E is linear.
Changing the the input signal u=unit step function to u=2*unitstep
function is actually changing the D.E. and a different linearity
definition should be used.....

Freinds, am I getting it now, or am I way off...?

Kindest regards,
Lasse

.

Relevant Pages

  • Re: Linearity question, is the proffesor wrong ?
    ... In this course we classify ODEs using the definition of ... should have been 10 according to linearity test. ... Linearity, as mathematicians apply it to a differential equation, ...
    (sci.math)
  • Re: Linearity question, is the proffesor wrong ?
    ... In this course we classify ODEs using the definition of ... should have been 10 according to linearity test. ... Linearity, as mathematicians apply it to a differential equation, ...
    (sci.math)