23.1.551 problem 541

Internal problem ID [5158]
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 : 541
Date solved : Tuesday, September 30, 2025 at 11:47:00 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 33

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

\[ y = c_1 \left (b +x \right )^{-\frac {b}{a -b}} \left (a +x \right )^{\frac {a}{a -b}} \]

✓ Mathematica. Time used: 0.064 (sec). Leaf size: 37

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

\begin{align*} y(x)&\to c_1 \exp \left (\int _1^x\frac {K[1]}{(a+K[1]) (b+K[1])}dK[1]\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.609 (sec). Leaf size: 27

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

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