72.2.15 problem 15 b(5)

Internal problem ID [14650]
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(5)
Date solved : Tuesday, January 28, 2025 at 06:46:22 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 {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 1.264 (sec). Leaf size: 39

dsolve([diff(S(t),t)=S(t)^3-2*S(t)^2+S(t),S(0) = -1/2],S(t), singsol=all)
 

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

✗ 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[0]==-1/2}},S[t],t,IncludeSingularSolutions -> True]
 

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