80.1.2 problem 3

Internal problem ID [18461]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter 1. section 5. Problems at page 19
Problem number : 3
Date solved : Monday, March 31, 2025 at 05:29:56 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 29

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

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

✓ Sympy. Time used: 0.120 (sec). Leaf size: 12

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

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