47.1.22 problem 22

Internal problem ID [7403]
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
Date solved : Monday, January 27, 2025 at 02:52:52 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{\sqrt {x}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

dsolve(diff(y(x),x)=sqrt(y(x))/sqrt(x),y(x), singsol=all)
 

\[ \sqrt {y}-\sqrt {x}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 26

DSolve[D[y[x],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*}