29.25.29 problem 726

Internal problem ID [5316]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 726
Date solved : Monday, January 27, 2025 at 11:09:00 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 18

dsolve((x-2*sqrt(x*y(x)))*diff(y(x),x) = y(x),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: 0.229 (sec). Leaf size: 33

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

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