dfsys1.py

Created on January 29, 2023

1.13 KB

Solves of the equation: dx/dt = ax(t) + by(t) dy/dt = ax(t) + by(t) with initial conditions x(0) = x0, y(0) = y0

from cmath import *
from matplotlib.pyplot import *
# 2023-01-28 EWS

# parameter input
print("systems of differential\nequations")
print("dx/dt=a*x+b*y")
print("dy/dt=c*x+d*y")
a=float(input("a? "))
b=float(input("b? "))
c=float(input("c? "))
d=float(input("d? "))
m=float(input("x0? "))
n=float(input("y0? "))


# characteristic roots
p=((a+d)+sqrt((a+d)**2-4*(a*d-b*c)))/2
q=((a+d)-sqrt((a+d)**2-4*(a*d-b*c)))/2

# set up result screen
axis((0,10,0,10))
axis("off")

# determine solutions
# best used for real solutions
if p!=q:
  r=(b*n+m*(p-d))/(p-q)
  s=m-r
  u=(c*m+n*(p-a))/(p-q)
  v=n-u
  text(0,9,"x=re**(pt)+se**(qt)")
  text(0,8.5,"r="+str(r))
  text(0,8,"p="+str(p))
  text(0,7.5,"s="+str(s))
  text(0,7,"q="+str(q))
  text(0,6,"y=ue**(pt)+se**(vt)")
  text(0,5.5,"u="+str(u))
  text(0,5,"p="+str(p))
  text(0,4.5,"v="+str(v))
  text(0,4,"q="+str(q))
else:
  r=(b*n+m*(p-d))
  s=m
  u=(c*m+n*(p-a))
  v=n
  text(0,9,"x=rte**(pt)+se**(pt)")
  text(0,8.5,"r="+str(r))
  text(0,8,"p="+str(p))
  text(0,7.5,"s="+str(s))
  text(0,6,"y=ute**(pt)+se**(vt)")
  text(0,5.5,"u="+str(u))
  text(0,5,"p="+str(p))
  text(0,4.5,"v="+str(v))

show()