function S=single_shot(alpha,beta,plot_soln)

dx = 1e-2;
y0=[0 0 alpha beta]';
y_sol=zeros(4,1/dx+1);
y_sol(:,1)=y0;
y=y0;

x=linspace(0,1,1/dx+1);
dx=x(2)-x(1);

for i=1:1/dx

    k1=dx.*RHS2(y,x(i));
    k2=dx.*RHS2(y+k1./2,x(i)+dx/2);
    k3=dx.*RHS2(y+k2./2,x(i)+dx/2);
    k4=dx.*RHS2(y+k3,x(i)+dx);
    
    y_new=y+(k1+2.*k2+2.*k3+k4)./6;
    
    y_sol(:,i+1)=y_new;
    
    y=y_new;
    
end

if plot_soln==1
    figure(1)
    hold on
    plot(x,y_sol(1,:),'.k')
    grid on
    box on
    xlabel('x')
    ylabel('w')
end

S=[y_sol(3,end);
y_sol(4,end)];