function Lab3_prob2
clear; clc; close all;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Problem 2
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
x=sym('x');
% Plotting a function. 
  function f=V1(x)
    f= heaviside(x)-heaviside(x-1) + heaviside(x-2)-heaviside(x-3) + heaviside(x-4)-heaviside(x-5);
  end
    figure;
    ezplot(V1(x), [0,10,-1,2])
    legend('Square wave')

  function f=V2(x)
    f= x.*(heaviside(x)-heaviside(x-1)) + (x-1).*(heaviside(x-1)-heaviside(x-2)) + (x-2).*(heaviside(x-2)-heaviside(x-3));
  end
    figure;
    ezplot(V2(x), [0,10,-1,2])
    legend('Saw-tooth wave')

  function f=V3(x)
    f= x.*(heaviside(x)-heaviside(x-1)) + (2-x).*(heaviside(x-1)-heaviside(x-3)) + (x-4).*(heaviside(x-3)-heaviside(x-5)) + + (6-x).*(heaviside(x-5)-heaviside(x-7));
  end
figure;
ezplot(V3(x), [0,10,-1,2])
legend('Triangular wave')

    function dy=myODE(x,y)
    % In order to solve a 2nd order ODE in Matlab, we need to turn it into
    % a system of 2 1st order ODEs.
    dy1=y(2); %y_1' = y_2
    dy2=-y(2)-3*y(1)+V1(x); % y_2' = the right hand side in y_1''
    dy=[dy1;dy2];
    end

% initial conditions y(0)=y0_1 and y'(0)=y0_2
y0=[0; 0];
x=0:0.1:10;
% Solving the ODE 
[x,y1]=ode45(@myODE, x, y0);
figure;
plot(x,y1(:,1),'-o')
legend('electric current under square wave applied voltage')


end