81.6.22 problem 7-21

Internal problem ID [21568]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 7. Linear Differential Equations. Page 101.
Problem number : 7-21
Date solved : Thursday, October 02, 2025 at 07:49:42 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

\[ y = -\frac {4 x^{2}}{x^{4}-4 c_1} \]

✓ Mathematica. Time used: 0.09 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to -\frac {4 x^2}{x^4-4 c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.126 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \frac {4 x^{2}}{C_{1} - x^{4}} \]