64.3.8 problem 9

Internal problem ID [13279]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page 37
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 05:14:15 AM
CAS classification : [_separable]

\begin{align*} \frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.055 (sec). Leaf size: 31

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

\begin{align*} s &= \frac {1}{2}-\frac {\sqrt {4 c_{1} t +1}}{2} \\ s &= \frac {1}{2}+\frac {\sqrt {4 c_{1} t +1}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.365 (sec). Leaf size: 47

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

\begin{align*} s(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {2 K[1]-1}{(K[1]-1) K[1]}dK[1]\&\right ][\log (t)+c_1] \\ s(t)\to 0 \\ s(t)\to 1 \\ \end{align*}