81.3.15 problem 4-20

Internal problem ID [21514]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 4. Homogeneous differential equations.
Problem number : 4-20
Date solved : Thursday, October 02, 2025 at 07:46:28 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 15

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

\[ y = -\sqrt {2 \ln \left (x \right )+4}\, x \]

✓ Mathematica. Time used: 0.119 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to -\sqrt {2} x \sqrt {\log (x)+2} \end{align*}

✗ Sympy

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

RecursionError : maximum recursion depth exceeded