11.2.2 problem 1.1-3 (b)

Internal problem ID [3426]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-3, page 6
Problem number : 1.1-3 (b)
Date solved : Tuesday, September 30, 2025 at 06:38:00 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (1\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 13

ode:=diff(y(t),t) = -y(t)^3; 
ic:=[y(1) = 3]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {3}{\sqrt {18 t -17}} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 16

ode=D[y[t],t]==-y[t]^3; 
ic=y[1]==3; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {3}{\sqrt {18 t-17}} \end{align*}

✓ Sympy. Time used: 0.246 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t)**3 + Derivative(y(t), t),0) 
ics = {y(1): 3} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {\sqrt {2} \sqrt {- \frac {1}{\frac {17}{18} - t}}}{2} \]