85.33.43 problem 43

Internal problem ID [22666]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 43
Date solved : Thursday, October 02, 2025 at 09:03:23 PM
CAS classification : [_quadrature]

\begin{align*} n^{\prime }&=-a n \end{align*}

With initial conditions

\begin{align*} n \left (0\right )&=n_{0} \\ \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 11

ode:=diff(n(t),t) = -a*n(t); 
ic:=[n(0) = n__0]; 
dsolve([ode,op(ic)],n(t), singsol=all);
 

\[ n = n_{0} {\mathrm e}^{-a t} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 13

ode=D[n[t],{t,1}]==-a*n[t]; 
ic={n[0]==n0}; 
DSolve[{ode,ic},n[t],t,IncludeSingularSolutions->True]
 

\begin{align*} n(t)&\to \text {n0} e^{-a t} \end{align*}

✓ Sympy. Time used: 0.064 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
a = symbols("a") 
n0 = symbols("n0") 
n = Function("n") 
ode = Eq(a*n(t) + Derivative(n(t), t),0) 
ics = {n(0): n0} 
dsolve(ode,func=n(t),ics=ics)
 

\[ n{\left (t \right )} = n_{0} e^{- a t} \]