Internal problem ID [12396]
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).
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: 0.047 (sec). Leaf size: 29
dsolve([diff(y(x),x)=sqrt(y(x))/x,y(-1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {i \ln \left (x \right ) \pi }{2}-i \pi -\frac {\pi ^{2}}{4}+\frac {\ln \left (x \right )^{2}}{4}+\ln \left (x \right )+1 \]
✓ Solution by Mathematica
Time used: 0.235 (sec). Leaf size: 43
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 i)^2 y(x)\to -\frac {1}{4} (i \log (x)+\pi +2 i)^2 \end{align*}