65.4.3 problem 3

Internal problem ID [15662]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 3
Date solved : Thursday, October 02, 2025 at 10:22:19 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

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

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

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 40

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

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

✓ Sympy. Time used: 0.144 (sec). Leaf size: 26

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

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