66.1.31 problem 34

Internal problem ID [15918]
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 1.2. page 33
Problem number : 34
Date solved : Thursday, October 02, 2025 at 10:30:02 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {1-y^{2}}{y} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-2 \\ \end{align*}

✓ Maple. Time used: 0.102 (sec). Leaf size: 16

ode:=diff(y(t),t) = (1-y(t)^2)/y(t); 
ic:=[y(0) = -2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -\sqrt {3 \,{\mathrm e}^{-2 t}+1} \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 20

ode=D[y[t],t]==(1-y[t]^2)/y[t]; 
ic={y[0]==-2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\sqrt {3 e^{-2 t}+1} \end{align*}

✓ Sympy. Time used: 0.393 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((y(t)**2 - 1)/y(t) + Derivative(y(t), t),0) 
ics = {y(0): -2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \sqrt {1 + 3 e^{- 2 t}} \]