Internal problem ID [12719]
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 (d).
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: 0.016 (sec). Leaf size: 12
dsolve([diff(y(x),x)=sqrt(y(x))/x,y(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\ln \left (x \right )+2\right )^{2}}{4} \]
✓ Solution by Mathematica
Time used: 0.151 (sec). Leaf size: 29
DSolve[{y'[x]==Sqrt[y[x]]/x,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} (\log (x)-2)^2 \\ y(x)\to \frac {1}{4} (\log (x)+2)^2 \\ \end{align*}