72.2.14 problem 15 b(4)

Internal problem ID [14649]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.3 page 47
Problem number : 15 b(4)
Date solved : Tuesday, January 28, 2025 at 06:46:18 AM
CAS classification : [_quadrature]

\begin{align*} S^{\prime }&=S^{3}-2 S^{2}+S \end{align*}

With initial conditions

\begin{align*} S \left (0\right )&={\frac {3}{2}} \end{align*}

✓ Solution by Maple

Time used: 1.247 (sec). Leaf size: 36

dsolve([diff(S(t),t)=S(t)^3-2*S(t)^2+S(t),S(0) = 3/2],S(t), singsol=all)
 

\[ S = {\mathrm e}^{\operatorname {RootOf}\left (-\ln \left ({\mathrm e}^{\textit {\_Z}}+1\right ) {\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} \ln \left (3\right )+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+t \,{\mathrm e}^{\textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}}+1\right )}+1 \]

✓ Solution by Mathematica

Time used: 0.560 (sec). Leaf size: 31

DSolve[{D[S[t],t]==S[t]^3-2*S[t]^2+S[t],{S[0]==3/2}},S[t],t,IncludeSingularSolutions -> True]
 

\[ S(t)\to \text {InverseFunction}\left [-\frac {1}{\text {$\#$1}-1}-\log (\text {$\#$1}-1)+\log (\text {$\#$1})\&\right ][t-2+\log (3)] \]