81.18.2 problem 22-2

Internal problem ID [21741]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 22. Electrical Circuits
Problem number : 22-2
Date solved : Thursday, October 02, 2025 at 08:01:41 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-k y&=A \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 20

ode:=diff(y(t),t)-k*y(t) = A; 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {-A +{\mathrm e}^{k t} \left (k +A \right )}{k} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 23

ode=D[y[t],t]-k*y[t]==A; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {A \left (e^{k t}-1\right )}{k}+e^{k t} \end{align*}

✓ Sympy. Time used: 0.082 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-A - k*y(t) + Derivative(y(t), t),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \frac {A}{k} + \frac {\left (A + k\right ) e^{k t}}{k} \]