87.4.15 problem 26

Internal problem ID [23281]
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 37
Problem number : 26
Date solved : Thursday, October 02, 2025 at 09:28:26 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} y^{\prime }-\frac {y}{x}&=-\frac {1}{2 y} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

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

\begin{align*} y &= \sqrt {x \left (c_1 x +1\right )} \\ y &= -\sqrt {x \left (c_1 x +1\right )} \\ \end{align*}

✓ Mathematica. Time used: 0.166 (sec). Leaf size: 42

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

\begin{align*} y(x)&\to -\sqrt {x} \sqrt {1+c_1 x}\\ y(x)&\to \sqrt {x} \sqrt {1+c_1 x} \end{align*}

✓ Sympy. Time used: 0.187 (sec). Leaf size: 26

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

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