9.4.8 problem 8

Internal problem ID [2921]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 8, page 34
Problem number : 8
Date solved : Tuesday, September 30, 2025 at 06:07:00 AM
CAS classification : [[_homogeneous, `class D`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \frac {2 x y-1}{y}+\frac {\left (x +3 y\right ) y^{\prime }}{y^{2}}&=0 \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 20

ode:=(2*x*y(x)-1)/y(x)+(x+3*y(x))/y(x)^2*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x}{3 \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {x^{2}}{3}} c_1 x}{3}\right )} \]

✓ Mathematica. Time used: 1.948 (sec). Leaf size: 37

ode=(2*x*y[x]-1)/y[x]+(x+3*y[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}{3 W\left (\frac {1}{3} x e^{\frac {1}{3} \left (x^2-c_1\right )}\right )}\\ y(x)&\to 0 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 3*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