jekyll-jupyter-notebook20210726-43262-rjr00q

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In [1]:

import sympy as sp

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sp.__version__

Out[2]:

'1.6.2'

Use `dsolve` in `sympy` to solve differential equations¶

In [3]:

from sympy.solvers.ode import dsolve

In [4]:

t = sp.var('t')
f = sp.Function('f')

In [16]:

f_ = sp.Derivative(f(t), t)

In [17]:

f_

Out[17]:

$\displaystyle \frac{d}{d t} f{\left(t \right)}$

In [18]:

f__ = sp.Derivative(f(t),t,t)

In [19]:

f__

Out[19]:

$\displaystyle \frac{d^{2}}{d t^{2}} f{\left(t \right)}$

In [20]:

ode = f__ - 4*f_ + 4
ode

Out[20]:

$\displaystyle - 4 \frac{d}{d t} f{\left(t \right)} + \frac{d^{2}}{d t^{2}} f{\left(t \right)} + 4$

In [21]:

dsolve(ode,f(t))

Out[21]:

$\displaystyle f{\left(t \right)} = C_{1} + C_{2} e^{4 t} + t$

In [24]:

dsolve(ode,f(t), ics={f(0):sp.E, f(4):sp.E})

Out[24]:

$\displaystyle f{\left(t \right)} = t + \frac{4 e^{4 t}}{1 - e^{16}} - \frac{4}{1 - e^{16}} + e$