66.4.5 problem 12

Internal problem ID [15969]
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 : 12
Date solved : Thursday, October 02, 2025 at 10:35:47 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

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

\[ y = \frac {1}{t +c_1} \]

✓ Mathematica. Time used: 0.057 (sec). Leaf size: 18

ode=D[y[t],t]==-y[t]^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{t-c_1}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.089 (sec). Leaf size: 7

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

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