Internal problem ID [12113]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {s^{2}-\sqrt {t}\, s^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 12
dsolve((1+s(t)^2)-sqrt(t)*diff(s(t),t)=0,s(t), singsol=all)
\[ s \left (t \right ) = \tan \left (2 \sqrt {t}+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.332 (sec). Leaf size: 30
DSolve[(1+s[t]^2)-Sqrt[t]*s'[t]==0,s[t],t,IncludeSingularSolutions -> True]
\begin{align*} s(t)\to \tan \left (2 \sqrt {t}+c_1\right ) s(t)\to -i s(t)\to i \end{align*}