71.8.10 problem 5 (c)

Internal problem ID [14373]
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 (c)
Date solved : Monday, March 31, 2025 at 12:19:54 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (1\right )&={\frac {1}{2}} \end{align*}

✓ Maple. Time used: 0.038 (sec). Leaf size: 11

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

\[ y = -\frac {1}{x -3} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 12

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

\[ y(x)\to \frac {1}{3-x} \]

✓ Sympy. Time used: 0.143 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = - \frac {1}{x - 3} \]