23.1.236 problem 232

Internal problem ID [4843]
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 : 232
Date solved : Tuesday, September 30, 2025 at 08:44:03 AM
CAS classification : [_linear]

\begin{align*} \left (a +x \right ) y^{\prime }&=b x +y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 22

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

\[ y = b \left (a +x \right ) \ln \left (a +x \right )+\left (b +c_1 \right ) a +c_1 x \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 27

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

\begin{align*} y(x)&\to (a+x) \left (-\frac {b x}{a+x}+b \log (a+x)+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.181 (sec). Leaf size: 29

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

\[ y{\left (x \right )} = C_{1} a + C_{1} x + a b \log {\left (a + x \right )} + a b + b x \log {\left (a + x \right )} \]