23.1.359 problem 344

Internal problem ID [4966]
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 : 344
Date solved : Tuesday, September 30, 2025 at 09:06:17 AM
CAS classification : [_separable]

\begin{align*} x \left (a x +1\right ) y^{\prime }+a -y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=x*(a*x+1)*diff(y(x),x)+a-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 x +a}{a x +1} \]

✓ Mathematica. Time used: 0.092 (sec). Leaf size: 78

ode=x*(1+a*x)D[y[x],x]+a-y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \exp \left (\int _1^x\frac {1}{a K[1]^2+K[1]}dK[1]\right ) \left (\int _1^x-\frac {a \exp \left (-\int _1^{K[2]}\frac {1}{a K[1]^2+K[1]}dK[1]\right )}{a K[2]^2+K[2]}dK[2]+c_1\right )\\ y(x)&\to a \end{align*}

✓ Sympy. Time used: 0.203 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a + x*(a*x + 1)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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