Internal problem ID [11613]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}}=0} \]
✓ Solution by Maple
Time used: 0.031 (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 \left (t \right ) = \frac {1}{2}-\frac {\sqrt {4 c_{1} t +1}}{2} s \left (t \right ) = \frac {1}{2}+\frac {\sqrt {4 c_{1} t +1}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 0.682 (sec). Leaf size: 59
DSolve[(2*s[t]-1)/t*s'[t]+(s[t]-s[t]^2)/t^2==0,s[t],t,IncludeSingularSolutions -> True]
\begin{align*} s(t)\to \frac {1}{2} \left (1-\sqrt {1-4 e^{c_1} t}\right ) s(t)\to \frac {1}{2} \left (1+\sqrt {1-4 e^{c_1} t}\right ) s(t)\to 0 s(t)\to 1 \end{align*}