66.4.6 problem 13

Internal problem ID [15970]
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 1.5 page 71
Problem number : 13
Date solved : Thursday, October 02, 2025 at 10:35:48 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.053 (sec). Leaf size: 11

ode:=diff(y(t),t) = y(t)^3; 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {1}{\sqrt {-2 t +1}} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 14

ode=D[y[t],t]==y[t]^3; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{\sqrt {1-2 t}} \end{align*}

✓ Sympy. Time used: 0.219 (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(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

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