89.6.27 problem 27

Internal problem ID [24410]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Miscellaneous Exercises at page 45
Problem number : 27
Date solved : Thursday, October 02, 2025 at 10:25:51 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.170 (sec). Leaf size: 36

ode:=x-y(x)+(3*x+y(x))*diff(y(x),x) = 0; 
ic:=[y(2) = -1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {x \left (2-\operatorname {LambertW}\left (2 x \,{\mathrm e}^{2 i \pi \_Z2 +4}\right )\right )}{\operatorname {LambertW}\left (2 x \,{\mathrm e}^{2 i \pi \_Z2 +4}\right )} \]

✓ Mathematica. Time used: 0.079 (sec). Leaf size: 32

ode=(x-y[x])+(3*x+y[x])*D[y[x],x]==0; 
ic={y[2]==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\log \left (\frac {y(x)}{x}+1\right )-\frac {2}{\frac {y(x)}{x}+1}=-\log (x)-4,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (3*x + y(x))*Derivative(y(x), x) - y(x),0) 
ics = {y(2): -1} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded