29.18.33 problem 511

Internal problem ID [5107]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 511
Date solved : Sunday, March 30, 2025 at 06:40:48 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x y y^{\prime }+2 x^{2}-2 x y-y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 19

ode:=x*y(x)*diff(y(x),x)+2*x^2-2*x*y(x)-y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \left (\operatorname {LambertW}\left ({\mathrm e}^{2 c_1 -1} x^{2}\right )+1\right ) \]

✓ Mathematica. Time used: 3.146 (sec). Leaf size: 25

ode=x y[x] D[y[x],x]+2 x^2-2 x y[x]-y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

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

RecursionError : maximum recursion depth exceeded