H1Q2b

t = 0:0.1:20;           
f = @(s) 3.*sin(2.*s)./sqrt(2.*s + 1);
 
Cs = [-2, 1, 4];    
Y = zeros(length(Cs), length(t));
 
for k = 1:length(Cs)
    C = Cs(k);
    Ivals = zeros(size(t));
    for j = 1:length(t)
        Ivals(j) = integral(f, 0, t(j));  
    end
    Y(k,:) = C.*exp(-t) + exp(-t).*Ivals;
end
 
figure;
plot(t, Y(1,:), '-','DisplayName','C = -2'); hold on;
plot(t, Y(2,:), '--','DisplayName','C = 1');
plot(t, Y(3,:), ':','DisplayName','C = 4');
xlabel('t'); ylabel('y(t)');
legend('Location','best'); grid on;