69.1.16 problem 16

Internal problem ID [14169]
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
Date solved : Tuesday, January 28, 2025 at 06:18:35 AM
CAS classification : [_separable]

\begin{align*} 1+s^{2}-\sqrt {t}\, s^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 12

dsolve((1+s(t)^2)-sqrt(t)*diff(s(t),t)=0,s(t), singsol=all)
 

\[ s = \tan \left (2 \sqrt {t}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.253 (sec). Leaf size: 47

DSolve[(1+s[t]^2)-Sqrt[t]*D[s[t],t]==0,s[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} s(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2+1}dK[1]\&\right ]\left [2 \sqrt {t}+c_1\right ] \\ s(t)\to -i \\ s(t)\to i \\ \end{align*}