63.3.5 problem 4(b)

Internal problem ID [13040]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.2 Antiderivatives. Exercises page 19
Problem number : 4(b)
Date solved : Tuesday, January 28, 2025 at 04:49:58 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=\frac {1}{t \ln \left (t \right )} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 9

dsolve(diff(x(t),t)=1/(t*ln(t)),x(t), singsol=all)
 

\[ x \left (t \right ) = \ln \left (\ln \left (t \right )\right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 11

DSolve[D[x[t],t]==1/(t*Log[t]),x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \log (\log (t))+c_1 \]