74.7.12 problem 12

Internal problem ID [16018]
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 : 12
Date solved : Monday, March 31, 2025 at 02:28:48 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{t +y}&=0 \end{align*}

✓ Maple. Time used: 0.080 (sec). Leaf size: 33

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

\[ y = \operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a} \left (\ln \left (\frac {1}{\textit {\_a}}\right ) \textit {\_a} +\ln \left (\frac {1}{\textit {\_a}}\right )+1\right )}d \textit {\_a} +\ln \left (t \right )+c_1 \right ) t \]

✓ Mathematica. Time used: 0.121 (sec). Leaf size: 39

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

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

✗ Sympy

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

Timed Out