ode; zero input response; drawing the function in matlab

hello

in the context of ordinary differential equations and system modelling, an example of how to determine the zero-input response from a system modelled by q(D) is

for which the answer is supposed to be

So when trying to prove to myself that the resulting plot for q(D) really was a constant 0, I tried this in matlab:

syms x 

y = exp(-x) * (cos(2*x) + 2*sin(2*x));

qD = (diff(y) + y)^2 + 4*y;

diffy = diff(y);

hold on

fplot(y, [0 5])
fplot(qD, [0 5])
fplot(diffy, [0 5])

legend ('y', 'qD', 'diffy') 

but the resulting curve for 'qD' is anything but 0;

so is my formula for the 'qD' curve wrong? or is the solution to the exercise wrong?

regards, Danny.

Answer 1

[Alan Stevens]

I think you should interpret (D+1)^2y as D^2y + 2Dy + y; i.e. d^2y/dt^2 + 2dy/dt + y

Currently you have it as (dy/dt)^2 +2dy/dt + y

[Danny Van Elsen]

indeed

qD = diff(y,2) + 2*diff(y) + 5*y;

does give me constant 0 result, thanks!!!