32.5.2 problem Exercise 11.2, page 97

Internal problem ID [5840]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number : Exercise 11.2, page 97
Date solved : Tuesday, March 04, 2025 at 11:47:52 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.046 (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: 0.126 (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)
 

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