23.1.235 problem 231

Internal problem ID [4842]
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 : 231
Date solved : Tuesday, September 30, 2025 at 08:44:02 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \int _1^x\frac {b K[1]}{a+K[1]}dK[1]+c_1 \end{align*}

✓ Sympy. Time used: 0.097 (sec). Leaf size: 14

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),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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