69.1.27 problem 44

Internal problem ID [14180]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 44
Date solved : Tuesday, January 28, 2025 at 06:19:15 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} 2 \sqrt {s t}-s+t s^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 18

dsolve((2*sqrt(s(t)*t)-s(t))+t*diff(s(t),t)=0,s(t), singsol=all)
 

\[ \frac {s}{\sqrt {s t}}+\ln \left (t \right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.176 (sec). Leaf size: 19

DSolve[(2*Sqrt[s[t]*t]-s[t])+t*D[s[t],t]==0,s[t],t,IncludeSingularSolutions -> True]
 

\[ s(t)\to \frac {1}{4} t (-2 \log (t)+c_1){}^2 \]