Internal problem ID [12718]
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 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {\sqrt {y}}{x}=0} \] With initial conditions \begin {align*} [y \left (-1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 28
dsolve([diff(y(x),x)=sqrt(y(x))/x,y(-1) = -1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\ln \left (x \right )^{2}}{4}+\frac {i \left (2-\pi \right ) \ln \left (x \right )}{2}-\frac {\left (-2+\pi \right )^{2}}{4} \]
✓ Solution by Mathematica
Time used: 0.151 (sec). Leaf size: 39
DSolve[{y'[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)^2 \\ y(x)\to -\frac {1}{4} (i \log (x)+\pi -2)^2 \\ \end{align*}