71.8.21 problem 8 (d)

Internal problem ID [14384]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number : 8 (d)
Date solved : Monday, March 31, 2025 at 12:20:43 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Maple. Time used: 0.099 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.086 (sec). Leaf size: 29

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

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

✗ Sympy

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

NotImplementedError : Initial conditions produced too many solutions for constants