47.1.23 problem 23

Internal problem ID [7404]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page 7
Problem number : 23
Date solved : Sunday, March 30, 2025 at 11:57:45 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: 0.125 (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: 0.231 (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)
 

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