72.2.13 problem 15 b(3)

Internal problem ID [14648]
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)
Date solved : Tuesday, January 28, 2025 at 06:46:14 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 )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ S = 1 \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 6

DSolve[{D[S[t],t]==S[t]^3-2*S[t]^2+S[t],{S[0]==1}},S[t],t,IncludeSingularSolutions -> True]
 

\[ S(t)\to 1 \]