71.8.19 problem 8 (b)

Internal problem ID [14453]
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 (b)
Date solved : Tuesday, January 28, 2025 at 06:31:44 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (-1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 5

dsolve([diff(y(x),x)=sqrt(y(x))/x,y(-1) = 0],y(x), singsol=all)
 

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.109 (sec). Leaf size: 24

DSolve[{D[y[x],x]==Sqrt[y[x]]/x,{y[-1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

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