72.2.12 problem 15 b(2)

Internal problem ID [14647]
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(2)
Date solved : Tuesday, January 28, 2025 at 06:46:09 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} S \left (1\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 1.713 (sec). Leaf size: 34

dsolve([diff(S(t),t)=S(t)^3-2*S(t)^2+S(t),S(1) = 1/2],S(t), singsol=all)
 

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

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[S[t],t]==S[t]^3-2*S[t]^2+S[t],{S[1]==1/2}},S[t],t,IncludeSingularSolutions -> True]
 

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