65.8.8 problem 5 (a)

Internal problem ID [15729]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number : 5 (a)
Date solved : Thursday, October 02, 2025 at 10:24:17 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 9

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

\[ y = -\frac {1}{x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 10

ode=D[y[x],x]==y[x]^2; 
ic={y[-1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{x} \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = - \frac {1}{x} \]