47.2.10 problem 10

Internal problem ID [7426]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 10
Date solved : Monday, January 27, 2025 at 02:54:55 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 21

dsolve((y(x)+sqrt(x*y(x)))-x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ -\frac {y}{\sqrt {x y}}+\frac {\ln \left (x \right )}{2}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.171 (sec). Leaf size: 17

DSolve[(y[x]+Sqrt[x*y[x]])-x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} x (\log (x)+c_1){}^2 \]