How to solve a second order linear differential equation with a heaviside function

I want to numerically solve the LDE (Linear Differential Equation) by integrating it numerically according to a flow diagram (see attached file). I have tried my best to come up with a script, but it does not give the correct answer.

clear all;

close all;

syms y(t) x(t) t

Dy = diff(y,t); D2y = diff(y,t,2); old = sympref ('HeavisideAtOrigin', 1);

cond = [y(0)==0, Dy(0)==0, D2y(0)==0];

eqn = diff(y,t,2) + 3*diff(y,t,1) + 2*y == heaviside(t);

ySol(t) = dsolve (eqn)

Answer 1

[Lateef Adewale Kareem]

Since its a second order differential equation, there is no need for y''(0)

and since you want to solve numerically, you can try this

Dy = diff(y,t); D2y = diff(y,t,2); old = sympref ('HeavisideAtOrigin', 1);

cond = [0, 0];

eqn = @(t,y) [y(2); -3*y(2)-2*y(1) + heaviside(t)]; [T,Y] = ode45(eqn,[0,20],cond)

visualize

plot(T,Y)