74.7.20 problem 20

Internal problem ID [16026]
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 : Monday, March 31, 2025 at 02:29:34 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.089 (sec). Leaf size: 30

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]
 

\[ \text {Solve}\left [\int _1^{\frac {y(t)}{t}}\frac {K[1]}{K[1]+1}dK[1]=\log (t)+c_1,y(t)\right ] \]

✗ 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