MATLAB: Ode; zero input response; drawing the function in matlab

MATLABodeplot

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.

Best Answer

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

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By adding 3 variables y4,y5 and y6 your system becomes a first order differential equations system.

%y4=dy1/dt, thus d2y1/dt2=dy4/dt
%y5=dy2/dt, thus d2y2/dt2=dy5/dt
%y6=dy3/dt, thus d2y3/dt2=dy6/dt
%The system of equation becomes
%dy1/dt=y11; 
%dy2/dt=y22; 
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function dy=myequ(t,y)
dy(1)=y(4)
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[t,y]=ode45(@myequ,tspan,y0)

Best Answer

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MATLAB: Please Help Me! i want to plot a equation dx/dt = y-5; dy/dt = -x+5; x(0)=0,y(0)=0. What type of code solver should i use.

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