87.1.22 problem 27

Internal problem ID [23234]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 9
Problem number : 27
Date solved : Thursday, October 02, 2025 at 09:24:42 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=diff(y(x),x) = 1/2*(x^2+y(x)^2)/x/y(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.115 (sec). Leaf size: 38

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

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

✓ Sympy. Time used: 0.242 (sec). Leaf size: 22

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

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