89.2.19 problem 19

Internal problem ID [24284]
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. Exercises at page 27
Problem number : 19
Date solved : Thursday, October 02, 2025 at 10:07:08 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} t \left (s^{2}+t^{2}\right ) s^{\prime }-s \left (s^{2}-t^{2}\right )&=0 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 33

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

\[ s = \frac {{\mathrm e}^{-2 c_1}}{\sqrt {\frac {{\mathrm e}^{-4 c_1}}{t^{4} \operatorname {LambertW}\left (\frac {{\mathrm e}^{-4 c_1}}{t^{4}}\right )}}\, t} \]

✓ Mathematica. Time used: 2.246 (sec). Leaf size: 49

ode=t*(s[t]^2+t^2)*D[s[t],t]-s[t]*(s[t]^2-t^2)==0; 
ic={}; 
DSolve[{ode,ic},s[t],t,IncludeSingularSolutions->True]
 

\begin{align*} s(t)&\to -t \sqrt {W\left (\frac {e^{2 c_1}}{t^4}\right )}\\ s(t)&\to t \sqrt {W\left (\frac {e^{2 c_1}}{t^4}\right )}\\ s(t)&\to 0 \end{align*}

✗ Sympy

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

RecursionError : maximum recursion depth exceeded