71.4.8 problem 8

Internal problem ID [14380]
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 : Tuesday, January 28, 2025 at 06:28:50 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.000 (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: 0.118 (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*}