23.1.5 problem 4

Internal problem ID [4612]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 4
Date solved : Tuesday, September 30, 2025 at 07:36:57 AM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 31

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

\[ y = \frac {{\mathrm e}^{c x} c_1 \,c^{2}+\left (-b x -a \right ) c -b}{c^{2}} \]

✓ Mathematica. Time used: 0.068 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to -\frac {a c+b c x+b}{c^2}+c_1 e^{c x} \end{align*}

✓ Sympy. Time used: 0.083 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = C_{1} e^{c x} - \frac {a}{c} - \frac {b x}{c} - \frac {b}{c^{2}} \]