65.4.8 problem 8

Internal problem ID [15667]
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 : 8
Date solved : Thursday, October 02, 2025 at 10:22:28 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

\[ \sqrt {y}-\frac {\ln \left (x \right )}{2}-c_1 = 0 \]

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 21

ode=D[y[x],x]==Sqrt[y[x]]/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{4} (\log (x)+c_1){}^2\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.118 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \frac {C_{1}^{2}}{4} + \frac {C_{1} \log {\left (x \right )}}{2} + \frac {\log {\left (x \right )}^{2}}{4} \]