65.1.3 problem 5.1 (iii)

Internal problem ID [13627]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 5, Trivial differential equations. Exercises page 33
Problem number : 5.1 (iii)
Date solved : Wednesday, March 05, 2025 at 10:05:33 PM
CAS classification : [_quadrature]

\begin{align*} u^{\prime }&=4 t \ln \left (t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=diff(u(t),t) = 4*t*ln(t); 
dsolve(ode,u(t), singsol=all);
 

\[ u = 2 \ln \left (t \right ) t^{2}-t^{2}+c_{1} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 20

ode=D[u[t],t]==4*t*Log[t]; 
ic={}; 
DSolve[{ode,ic},u[t],t,IncludeSingularSolutions->True]
 

\[ u(t)\to -t^2+2 t^2 \log (t)+c_1 \]

✓ Sympy. Time used: 0.142 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
u = Function("u") 
ode = Eq(-4*t*log(t) + Derivative(u(t), t),0) 
ics = {} 
dsolve(ode,func=u(t),ics=ics)
 

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