23.1.159 problem 159

Internal problem ID [4766]
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 : 159
Date solved : Tuesday, September 30, 2025 at 08:30:54 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

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

\[ y = -\frac {x^{n} b}{c -n}-\frac {a}{c}+x^{c} c_1 \]

✓ Mathematica. Time used: 0.57 (sec). Leaf size: 31

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

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

✗ Sympy

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

RecursionError : maximum recursion depth exceeded