# Solvers

Boilerplate to make the doctester work. 


```
import sys
import os
sys.path.insert(1, os.path.join(os.path.pardir, "ipython_doctester"))
from sympy import *
from ipython_doctester import test
# Work around a bug in IPython. This will disable the ability to paste things with >>>
def notransform(line): return line
from IPython.core import inputsplitter
inputsplitter.transform_classic_prompt = notransform
init_printing()
```

For each exercise, fill in the function according to its docstring. Execute the cell to see if you did it right. 


```
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).


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

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


```
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.


```

```

If the population growth is bounded, it is modeled by 

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


```

```

f1e5c0baf221ac427f3141658b5b8f4a24dd4276
ipynb
Jupyter Notebook
tutorial_exercises/Solvers.ipynb
certik/scipy-2013-tutorial
26a1cab3a16402afdc20088cedf47acd9bc58483
BSD-3-Clause
2015-02-28T08:53:05.000Z
2021-12-05T05:37:59.000Z
sympy/Solvers.ipynb
certik/scipy-in-13
418c139ab6e1b0c9acd53e7e1a02b8b930005096
BSD-3-Clause
2021-04-17T15:05:46.000Z
2021-04-17T15:05:46.000Z
sympy/Solvers.ipynb
certik/scipy-in-13
418c139ab6e1b0c9acd53e7e1a02b8b930005096
BSD-3-Clause
2015-03-11T00:25:21.000Z
2021-08-25T14:52:40.000Z
Qwen/Qwen-72B
1. YES
2. YES