Solvers

In [ ]:
from sympy import *
init_printing()

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

In [ ]:
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 solve(a*x**2 + b*x + c, x)
quadratic()

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

In [ ]:
def cubic():
    return solve(x**3 + a*x**2 + b*x + c, x)
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.

In [ ]:
dsolve(f(t).diff(t) - a*f(t), f(t))

If the population growth is bounded, it is modeled by

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

Solve this differential equation using SymPy.

In [ ]:
dsolve(f(t).diff(t) - f(t)*(1 - f(t)), f(t))