69.1.28 problem 45

Internal problem ID [14181]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 45
Date solved : Tuesday, January 28, 2025 at 06:19:22 AM
CAS classification : [_linear]

\begin{align*} t -s+t s^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 12

dsolve((t-s(t))+t*diff(s(t),t)=0,s(t), singsol=all)
 

\[ s = \left (c_{1} -\ln \left (t \right )\right ) t \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 14

DSolve[(t-s[t])+t*D[s[t],t]==0,s[t],t,IncludeSingularSolutions -> True]
 

\[ s(t)\to t (-\log (t)+c_1) \]