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 : Monday, January 27, 2025 at 02:53:02 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(diff(y(x),x)=sqrt(y(x))/x,y(x), singsol=all)
 

\[ \sqrt {y}-\frac {\ln \left (x \right )}{2}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.125 (sec). Leaf size: 21

DSolve[D[y[x],x]==Sqrt[y[x]]/x,y[x],x,IncludeSingularSolutions -> True]
 

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