Internal problem ID [12592]
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(3).
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*} [S \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 5
dsolve([diff(S(t),t)=S(t)^3-2*S(t)^2+S(t),S(0) = 1],S(t), singsol=all)
\[ S \left (t \right ) = 1 \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 6
DSolve[{S'[t]==S[t]^3-2*S[t]^2+S[t],{S[0]==1}},S[t],t,IncludeSingularSolutions -> True]
\[ S(t)\to 1 \]