88.1.6 problem 20

Internal problem ID [23949]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 1. Introduction. Exercise at page 6
Problem number : 20
Date solved : Thursday, October 02, 2025 at 09:46:44 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 18

ode:=diff(y(t),t) = t*ln(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {t^{2} \ln \left (t \right )}{2}-\frac {t^{2}}{4}+c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 24

ode=D[y[t],t]==t*Log[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {t^2}{4}+\frac {1}{2} t^2 \log (t)+c_1 \end{align*}

✓ Sympy. Time used: 0.107 (sec). Leaf size: 17

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

\[ y{\left (t \right )} = C_{1} + \frac {t^{2} \log {\left (t \right )}}{2} - \frac {t^{2}}{4} \]