71.8.18 problem 8 (a)

Internal problem ID [14452]
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 : Tuesday, January 28, 2025 at 06:31:42 AM
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*}

✓ Solution by Maple

Time used: 0.136 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

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

DSolve[{D[y[x],x]==Sqrt[y[x]]/x,{y[-1]==1}},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*}