23.1.452 problem 442

Internal problem ID [5059]
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 : 442
Date solved : Tuesday, September 30, 2025 at 11:30:47 AM
CAS classification : [[_homogeneous, `class D`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x -y\right ) y^{\prime }&=\left (1+2 x y\right ) y \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 18

ode:=(x-y(x))*diff(y(x),x) = (1+2*x*y(x))*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x}{\operatorname {LambertW}\left (-{\mathrm e}^{x^{2}} c_1 x \right )} \]

✓ Mathematica. Time used: 4.149 (sec). Leaf size: 30

ode=(x-y[x])*D[y[x],x]==(1+2*x*y[x])*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x}{W\left (x \left (-e^{x^2-1-c_1}\right )\right )}\\ y(x)&\to 0 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x - y(x))*Derivative(y(x), x) - (2*x*y(x) + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out