89.6.17 problem 17

Internal problem ID [24400]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Miscellaneous Exercises at page 45
Problem number : 17
Date solved : Thursday, October 02, 2025 at 10:25:03 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(x),x)+a*y(x) = b; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 29

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

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

✓ Sympy. Time used: 0.068 (sec). Leaf size: 12

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

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