47.2.21 problem 21

Internal problem ID [7437]
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 : 21
Date solved : Monday, January 27, 2025 at 02:57:46 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y+\left (2 \sqrt {y x}-x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 18

dsolve(y(x)+(2*sqrt(x*y(x))-x)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.233 (sec). Leaf size: 33

DSolve[y[x]+(2*Sqrt[x*y[x]]-x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {2}{\sqrt {\frac {y(x)}{x}}}+2 \log \left (\frac {y(x)}{x}\right )=-2 \log (x)+c_1,y(x)\right ] \]