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 : Tuesday, March 04, 2025 at 04:38:46 PM
CAS classification : [_quadrature]

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

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

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

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

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

ode=D[y[t],t]==y[t]^3-y[t]^2; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.309 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t)**3 + y(t)**2 + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ t - \log {\left (y{\left (t \right )} - 1 \right )} + \log {\left (y{\left (t \right )} \right )} - \frac {1}{y{\left (t \right )}} = C_{1} \]