65.1.3 problem 5.1 (iii)

Internal problem ID [13706]
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 : Tuesday, January 28, 2025 at 05:55:42 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[u[t],t]==4*t*Log[t],u[t],t,IncludeSingularSolutions -> True]
 

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