71.8.18 problem 8 (a)

Internal problem ID [14381]
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 (a)
Date solved : Monday, March 31, 2025 at 12:20:29 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: 0.096 (sec). Leaf size: 27

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

\[ y = -\frac {i \pi \ln \left (x \right )}{2}+\frac {\ln \left (x \right )^{2}}{4}-\frac {\pi ^{2}}{4}-i \pi +\ln \left (x \right )+1 \]

✓ Mathematica. Time used: 0.138 (sec). Leaf size: 43

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} (i \log (x)+\pi -2 i)^2 \\ y(x)\to -\frac {1}{4} (i \log (x)+\pi +2 i)^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