90.5.4 problem 4

Internal problem ID [25123]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 71
Problem number : 4
Date solved : Thursday, October 02, 2025 at 11:51:02 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.818 (sec). Leaf size: 19

ode=D[y[t],{t,1}] == (y[t]^2+2*y[t]*t)/(t^2+t*y[t]); 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to t W\left (e^{c_1} t\right )\\ y(t)&\to 0 \end{align*}

✗ Sympy

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

RecursionError : maximum recursion depth exceeded