86.2.13 problem 13

Internal problem ID [23087]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 3. Some standard types of differential equations. Exercise 3c at page 50
Problem number : 13
Date solved : Thursday, October 02, 2025 at 09:19:46 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 28

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

\begin{align*} y &= \sqrt {2 \ln \left (x \right )+c_1}\, x \\ y &= -\sqrt {2 \ln \left (x \right )+c_1}\, x \\ \end{align*}

✓ Mathematica. Time used: 0.112 (sec). Leaf size: 36

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

\begin{align*} y(x)&\to -x \sqrt {2 \log (x)+c_1}\\ y(x)&\to x \sqrt {2 \log (x)+c_1} \end{align*}

✓ Sympy. Time used: 0.225 (sec). Leaf size: 29

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 = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - x \sqrt {C_{1} + 2 \log {\left (x \right )}}, \ y{\left (x \right )} = x \sqrt {C_{1} + 2 \log {\left (x \right )}}\right ] \]