72.2.27 problem 20

Internal problem ID [14591]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.3 page 47
Problem number : 20
Date solved : Monday, March 31, 2025 at 12:39:25 PM
CAS classification : [_quadrature]

\begin{align*} v^{\prime }&=-\frac {v}{R C} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=diff(v(t),t) = -v(t)/R/C; 
dsolve(ode,v(t), singsol=all);
 

\[ v = c_1 \,{\mathrm e}^{-\frac {t}{R C}} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 24

ode=D[ v[t],t]==-v[t]/(r*c); 
ic={}; 
DSolve[{ode,ic},v[t],t,IncludeSingularSolutions->True]
 

\begin{align*} v(t)\to c_1 e^{-\frac {t}{c r}} \\ v(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.116 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
C = symbols("C") 
R = symbols("R") 
v = Function("v") 
ode = Eq(Derivative(v(t), t) + v(t)/(C*R),0) 
ics = {} 
dsolve(ode,func=v(t),ics=ics)
 

\[ v{\left (t \right )} = C_{1} e^{- \frac {t}{C R}} \]