%Differential Equation: dy/dx=y-(1/2)*exp(x/2).*sin(5*x)+5*exp(x/2).*cos(5*x); y(0)=0; f=@(x,y) y-(1/2)*exp(x/2).*sin(5*x)+5*exp(x/2).*cos(5*x); f1=@(x,y) exp(x/2).*sin(5*x); %Analytic Solution xinit=0; yinit=0; %y(xinit)=yinit {y(0)=0} xmax=5; x=xinit:0.1:xmax; h=x(2)-x(1); m=length(x); y=zeros(1,m); y(1)=yinit; for n=1:m-1 y(n+1)=y(n)+h*f(x(n),y(n)); end; yy=exp(x/2).*sin(5*x); %Analytic Solution hold on; plot(x,y,'bo-','LineWidth',1.5); plot(x,yy,'r-','LineWidth',2.5); title('Euler Method','fontsize',14,'fontweight','bold'); legend('Euler Method','Analytic','Location','NorthWest'); grid on; hold off;