47.1.17 problem 17

Internal problem ID [7398]
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 : 17
Date solved : Monday, January 27, 2025 at 02:52:09 PM
CAS classification : [_separable]

\begin{align*} \frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

dsolve(1/sqrt(x)+diff(y(x),x)/sqrt(y(x))=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.143 (sec). Leaf size: 21

DSolve[1/Sqrt[x]+D[y[x],x]/Sqrt[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} \left (-2 \sqrt {x}+c_1\right ){}^2 \]