90.4.11 problem 12

Internal problem ID [25106]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 59
Problem number : 12
Date solved : Thursday, October 02, 2025 at 11:50:21 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+a y&=b \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=diff(y(t),t)+a*y(t) = b; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {b}{a}+{\mathrm e}^{-a t} c_1 \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 29

ode=D[y[t],{t,1}] +a*y[t]== b; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {b}{a}+c_1 e^{-a t}\\ y(t)&\to \frac {b}{a} \end{align*}

✓ Sympy. Time used: 0.069 (sec). Leaf size: 12

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

\[ y{\left (t \right )} = C_{1} e^{- a t} + \frac {b}{a} \]