#
#  Euler.py
#  
#
#  Created by Jason Francis on 3/16/08.
#  Solves First Order ODEs using Euler's method
#
import math  #needed for the floor function

#first, we need to get the differential equation
deq = raw_input("y' = ")

#and the initial x and y
x = float(raw_input("x(0) = "))
y = float(raw_input("y(0) = "))

#this sets up our IVP, but we still need some more information

step = float(raw_input("Step size: "))	#spacing from x_n to x_n+1
iterations = int(math.floor(float(raw_input("Iterations: ")))) #how many steps do we want to take?

m = eval(deq)	#executing a string like this is a terrible idea

#We need to store the values of x and y, so open a file stream
fout = open('output.eul','w')
fout.write(str(x) + "\t" + str(y) + "\n")

#time for the actual solving
for n in range(0,iterations):
	x = x + step
	y = y + step*m
	m = eval(deq)
	fout.write(str(x) + "\t" + str(y) + "\n")
	n = n+1
#####
fout.close()


exit