20.1.4 problem Problem 10

Internal problem ID [3561]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 10
Date solved : Sunday, March 30, 2025 at 01:51:02 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 9

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

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

✓ Mathematica. Time used: 0.095 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.152 (sec). Leaf size: 7

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

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