89.5.25 problem 25 (n=0)

Internal problem ID [24375]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 43
Problem number : 25 (n=0)
Date solved : Thursday, October 02, 2025 at 10:22:36 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.106 (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)
 

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