# Solvers


```python
from sympy import *
from sympy.solvers.solveset import solveset
init_printing()
```

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


```python
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).


```python
def quadratic():
    return ???
quadratic()
```

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


```python
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.


```python

```

If the population growth is bounded, it is modeled by 

$$f'(t) = f(t)(1 - f(t))$$

Solve this differential equation using SymPy.


```python

```

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tutorial_exercises/Advanced-Solvers.ipynb
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