# 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.

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def quadratic():
return ???


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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