#!/usr/bin/env python
# coding: utf-8

# # Solvers

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from sympy import *
init_printing()


# For each exercise, fill in the function according to its docstring. 

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a, b, c, d, x, y, z, t = symbols('a b c d x y z t')
f, g, h = symbols('f g h', cls=Function)


# ## Algebraic Equations

# Write a function that computes the [quadratic equation](http://en.wikipedia.org/wiki/Quadratic_equation).

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def quadratic():
    return ???
quadratic()


# Write a function that computes the general solution to the cubic $x^3 + ax^2 + bx + c$.

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def cubic():
    return ???
cubic()


# ## Differential Equations

# A population that grows without bound is modeled by the differential equation
# 
# $$f'(t)=af(t)$$
# 
# Solve this differential equation using SymPy.

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# If the population growth is bounded, it is modeled by 
# 
# $$f'(t) = f(t)(1 - f(t))$$
# 
# Solve this differential equation using SymPy.

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