17.5.3 problem 1.1-6 (c)

Internal problem ID [3436]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-6, page 7
Problem number : 1.1-6 (c)
Date solved : Monday, January 27, 2025 at 07:36:38 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{3}-y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.279 (sec). Leaf size: 16

dsolve(diff(y(t),t)=y(t)^3-y(t)^2,y(t), singsol=all)
 

\[ y = \frac {1}{\operatorname {LambertW}\left (-c_{1} {\mathrm e}^{-1+t}\right )+1} \]

✓ Solution by Mathematica

Time used: 0.239 (sec). Leaf size: 38

DSolve[D[y[t],t]==y[t]^3-y[t]^2,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \text {InverseFunction}\left [\frac {1}{\text {$\#$1}}+\log (1-\text {$\#$1})-\log (\text {$\#$1})\&\right ][t+c_1] \\ y(t)\to 0 \\ y(t)\to 1 \\ \end{align*}