38.2.34 problem 32 (a)

Internal problem ID [8252]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 32 (a)
Date solved : Tuesday, September 30, 2025 at 05:20:25 PM
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: 0.010 (sec). Leaf size: 11

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

\[ y = -\frac {1}{x -2} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 12

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}{2-x} \end{align*}

✓ Sympy. Time used: 0.075 (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} 
dsolve(ode,func=y(x),ics=ics)
 

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