83.16.2 problem 1 (b)

Internal problem ID [22043]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Examination I. page 253
Problem number : 1 (b)
Date solved : Thursday, October 02, 2025 at 08:22:42 PM
CAS classification : [[_homogeneous, `class D`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 18

ode:=2*x+1/y(x)+(1/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: 3.726 (sec). Leaf size: 29

ode=(2*x+1/y[x])+(1/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-c_1}\right )\right )}\\ y(x)&\to 0 \end{align*}

✗ Sympy

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

Timed Out