31.1.8 problem 3.2

Internal problem ID [5706]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 2
Problem number : 3.2
Date solved : Monday, January 27, 2025 at 01:09:08 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.254 (sec). Leaf size: 33

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

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