Question

using ZIR and 5.1 Use Matlab to find and plot the total response for the differential equation ZSR approach. (D2 +5D 6)y(t)x() where x(t) e-2t sin( 10t) u(t), and the initial conditions are: yo (0)-1 and уо (0)-2.
I NEED THE MATLAB CODE NOT THE ANALYTICAL SOLUTION !!!!

Answer 1

Hello,
          Please find the answer attached as under. Please give a thumbs up rating if you find the answer useful! Have a rocking day ahead!

****************** Matlab Code *******************

%%%%%%%%%%%%%%%%%%%%%%
%% solving differential equations

syms y(t)
Dy = diff(y);
ode = diff(y,t,2)+5*diff(y,t)+6 == exp(-t)*sin(10*t);
cond1 = y(0) == 1;
cond2 = Dy(0) == 2;
conds = [cond1 cond2];
ySol(t) = dsolve(ode,conds);
ySol = simplify(ySol);
ezplot(ySol(t))
xlabel('Time(s)');

************ End of Code **************

Output:

y = 191/2525 - (953*exp(-5*t))/1450 - (15*cos(10*t)*exp(-t))/5858 - (26*sin(10*t)*exp(-t))/2929 - (6*t)/5

Plot:

1010 ...- (exp(t) (375 cos(10 t)+1300 sin (10 t) 243078 exp(t) +175740 t exp(t)))/146450 D.5 1.5 -2 2.5 1 -6 -2

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