% Solve the initial value problem:
% y''+4y = dirac(t-3)
% y(0)=0, y'(0)=0

clear
syms s t Y

f=dirac(t-3);
F = laplace(f,t,s);

% Laplace transform of y' and y'':
Y1 = s*Y - 0;
Y2 = s*Y1 - 0;

% Solve for Laplace transform, Y(s):
Sol = simplify(solve(Y2 + 4*Y -F, Y))

% Inverse transform to obtain y(t):
sol = ilaplace(Sol,s,t)

% Plot solution
ezplot(sol,[0 10 -2 2])