23.1.177 problem 177

Internal problem ID [4784]
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 : 177
Date solved : Tuesday, September 30, 2025 at 08:36:02 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ y = -\frac {2 x}{x^{2}-2 c_1} \]

✓ Mathematica. Time used: 0.081 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to -\frac {2 x}{x^2-2 c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.112 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \frac {2 x}{C_{1} - x^{2}} \]