Internal problem ID [4982]
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: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\sqrt {y}}{\sqrt {x}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x)=sqrt(y(x))/sqrt(x),y(x), singsol=all)
\[ \sqrt {y \relax (x )}-\sqrt {x}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.232 (sec). Leaf size: 26
DSolve[y'[x]==Sqrt[y[x]]/Sqrt[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (2 \sqrt {x}+c_1\right ){}^2 \\ y(x)\to 0 \\ \end{align*}