Internal problem ID [12593]
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).
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 {3}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.25 (sec). Leaf size: 41
dsolve([diff(S(t),t)=S(t)^3-2*S(t)^2+S(t),S(0) = 3/2],S(t), singsol=all)
\[ S \left (t \right ) = {\mathrm e}^{\operatorname {RootOf}\left ({\mathrm e}^{\textit {\_Z}} \ln \left (3\right )-\ln \left ({\mathrm e}^{\textit {\_Z}}+1\right ) {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+t \,{\mathrm e}^{\textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}}+1\right )}+1 \]
✓ Solution by Mathematica
Time used: 0.885 (sec). Leaf size: 31
DSolve[{S'[t]==S[t]^3-2*S[t]^2+S[t],{S[0]==3/2}},S[t],t,IncludeSingularSolutions -> True]
\[ S(t)\to \text {InverseFunction}\left [-\frac {1}{\text {$\#$1}-1}-\log (\text {$\#$1}-1)+\log (\text {$\#$1})\&\right ][t-2+\log (3)] \]