I am facing problems in solving this question... I put my code .. please help

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]

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?

Answer 1

[Sulaymon Eshkabilov]

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)