x,y,l=var('x','y','l')
# x = Red Divisions
# y = Blue Divisions
# l = Blue advantage in effectiveness(lambda)

l=3.0    # given lambda
x_0=5.0  # initial red
y_0=2.0  # initial blue
deltat=0.1  # time step
w=.9   # given w

dxdt(x,y)=-l*w*.05*y-l*.005*x*y
dydt(x,y)=-w*.05*x-.005*x*y

War=[]

data=[[0,x_0,y_0]]  #initial (t,x,y)
t=0
x=x_0
y=y_0
for i in range(100000):
    deltax=dxdt(x,y)*deltat
    deltay=dydt(x,y)*deltat
    t+=deltat
    x+=deltax
    y+=deltay
    data.append([t,x,y])
    if x<0:
        War.append([round(l,1),"Blue",round(t,2),y])
        break
    if y<0:
        War.append([round(l,1),"Red",round(t,2),x])
        break
        
        
display(table(War,header_row=["$\\lambda$","Winner", "Time","Troops"]))