Internal problem ID [12914]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {S^{\prime }-S^{3}+2 S^{2}-S=0} \] With initial conditions \begin {align*} \left [S \left (0\right ) = -{\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.61 (sec). Leaf size: 45
dsolve([diff(S(t),t)=S(t)^3-2*S(t)^2+S(t),S(0) = -1/2],S(t), singsol=all)
\[ S \left (t \right ) = {\mathrm e}^{\operatorname {RootOf}\left (-3 \ln \left ({\mathrm e}^{\textit {\_Z}}+1\right ) {\mathrm e}^{\textit {\_Z}}-3 \,{\mathrm e}^{\textit {\_Z}} \ln \left (3\right )+3 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+3 t \,{\mathrm e}^{\textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}}+3\right )}+1 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{S'[t]==S[t]^3-2*S[t]^2+S[t],{S[0]==-1/2}},S[t],t,IncludeSingularSolutions -> True]
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