74.7.30 problem 30

Internal problem ID [16036]
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 : 30
Date solved : Monday, March 31, 2025 at 02:33:51 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 60.154 (sec). Leaf size: 19

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

\[ y(t)\to t \left (1+W\left (\frac {\log (t)+c_1}{e}\right )\right ) \]

✗ Sympy

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

TypeError : cannot determine truth value of Relational