32.3.2 problem Exact Differential equations. Exercise 9.5, page 79

Internal problem ID [5800]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 9
Problem number : Exact Differential equations. Exercise 9.5, page 79
Date solved : Sunday, March 30, 2025 at 10:18:15 AM
CAS classification : [[_homogeneous, `class D`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \frac {2 x y+1}{y}+\frac {\left (y-x \right ) y^{\prime }}{y^{2}}&=0 \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 18

ode:=(2*x*y(x)+1)/y(x)+(y(x)-x)/y(x)^2*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 4.989 (sec). Leaf size: 30

ode=(2*x*y[x]+1)/y[x]+(y[x]-x)/y[x]^2*D[y[x],x]==0; 
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)/y(x)**2 + (2*x*y(x) + 1)/y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out