Internal problem ID [5730]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\frac {y^{\prime }}{\sqrt {y}}=-\frac {1}{\sqrt {x}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(1/sqrt(x)+diff(y(x),x)/sqrt(y(x))=0,y(x), singsol=all)
\[ \sqrt {y \left (x \right )}+\sqrt {x}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.125 (sec). Leaf size: 21
DSolve[1/Sqrt[x]+y'[x]/Sqrt[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (-2 \sqrt {x}+c_1\right ){}^2 \]