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Rama a on 7 Jun 2021
I am facing problems in solving this question .. I will put my code and please help me to correct my working
Consider the following Differential Equation
diff(y,t,2) + A*diff(y,t) + B == C + 5*cos(1500*t)
A-Solve it (write code) for t≥0 using zero initial conditions.
B- Determine the response of the LTI systems for the given input and initial conditions: y (0)= 0, dy/dt(0) =A
A=3 B=4 C=4
syms t y(t) %symbolic variable
A = 3; B = 4; C = 4;
ode = diff(y,t,2) + A*diff(y,t) + B == C + 5*cos(1500*t); %given eqn
con1 = y(0) == 0; %y(0)
Dy(t) = diff(y,t); %y'(t)
con2 = Dy(0) == 3; %y'(0)
solution = dsolve(ode,[con1 con2]) %output y(t)
digits(3); %precision
simpleSolution = simplify(vpa(solution)) %simplified representation
fplot(solution, [0 20])
hold on
fplot(Dy(t), [0 20])
hold off
xlabel("t ->");ylabel("y(t) ->");title("Output");
Walter Roberson on 8 Jun 2021
You seem to have already solved the first part?
It is not clear to me which LTI system is being referred to for the second part?

Sulaymon Eshkabilov on 8 Jun 2021
What are the LTI system and the input signal ?
LTI system simulation can be done easily with: tf() and lsim(). Example:
A = 1; B = 2; C = 3;
TF = tf(1, [A B C]); % LTI system: A*DDy + B*Dy + C*y = u(t)
t = linspace(0, 1, 2000);
u = cos(t);
[R, time] = lsim(TF, u, t);
plot(time, R)