68.7.20 problem 20

Internal problem ID [17384]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 20
Date solved : Thursday, October 02, 2025 at 02:15:35 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} t^{2}+y t +y^{2}-t y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 23

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

\[ y = -\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_1 -1}}{t}\right ) t -t \]

✓ Mathematica. Time used: 1.193 (sec). Leaf size: 31

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

\begin{align*} y(t)&\to -t \left (1+W\left (-\frac {e^{-1-c_1}}{t}\right )\right )\\ y(t)&\to -t \end{align*}

✗ Sympy

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

RecursionError : maximum recursion depth exceeded