Internal problem ID [12444]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {2 \sqrt {s t}-s+t s^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve((2*sqrt(s(t)*t)-s(t))+t*diff(s(t),t)=0,s(t), singsol=all)
\[ \frac {s \left (t \right )}{\sqrt {s \left (t \right ) t}}+\ln \left (t \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.315 (sec). Leaf size: 19
DSolve[(2*Sqrt[s[t]*t]-s[t])+t*s'[t]==0,s[t],t,IncludeSingularSolutions -> True]
\[ s(t)\to \frac {1}{4} t (-2 \log (t)+c_1){}^2 \]