89.1.6 problem 6

Internal problem ID [24241]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 21
Problem number : 6
Date solved : Thursday, October 02, 2025 at 10:01:20 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

\[ y = -\frac {2}{x^{2}-2 c_1} \]

✓ Mathematica. Time used: 0.069 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to -\frac {2}{x^2+2 c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.081 (sec). Leaf size: 10

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

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