85.12.10 problem 10

Internal problem ID [22504]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 40
Problem number : 10
Date solved : Thursday, October 02, 2025 at 08:43:37 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

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

ode:=diff(y(x),x) = 1/2*x/y(x)+1/2*y(x)/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: 0.119 (sec). Leaf size: 38

ode=D[y[x],x]==1/2*(x/y[x]+y[x]/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: 0.175 (sec). Leaf size: 22

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

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