clear all;
close all;
clc;

pkg load symbolic;
syms s(t);

DJ = diff(s,t,2) + 3*diff(s,t) + 2*s == 1;
sol = dsolve (DJ, s(0) == 0, diff(s)(0) ==0 )
latex(sol)

s = rhs(sol) * heaviside(t)

h1 = diff(s)
h = diff(h1) + 2*h1
h_fact = factor(h, dirac(t), diff(dirac(t)), heaviside(t))
latex( h_fact )

subs(h, t, 0)
h = subs( h_fact, [dirac(t), diff(dirac(t))], [0,0] ) 

syms tau
y = int( subs(h, t, tau) * exp(t-tau), tau, 0, t )

latex(y)