Internal problem ID [5736]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.1 Separable equations problems.
page 7
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {\sqrt {y}}{x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(y(x),x)=sqrt(y(x))/x,y(x), singsol=all)
\[ \sqrt {y \left (x \right )}-\frac {\ln \left (x \right )}{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 21
DSolve[y'[x]==Sqrt[y[x]]/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} (\log (x)+c_1){}^2 y(x)\to 0 \end{align*}