23.1.731 problem 729

Internal problem ID [5338]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 729
Date solved : Tuesday, September 30, 2025 at 12:30:49 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 84

ode:=diff(y(x),x)*(x*y(x))^(1/2)+x-y(x) = (x*y(x))^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {\left (3 x -3 \sqrt {x y}\right ) \ln \left (-x +\sqrt {x y}\right )+\left (x -\sqrt {x y}\right ) \ln \left (\sqrt {x y}+x \right )+\left (c_1 +2 \ln \left (x \right )\right ) \sqrt {x y}-x \left (c_1 +2 \ln \left (x \right )-2\right )}{x -\sqrt {x y}} = 0 \]

✓ Mathematica. Time used: 0.092 (sec). Leaf size: 62

ode=D[y[x],x]*Sqrt[x*y[x]]+x -y[x]==Sqrt[x*y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {1}{1-\sqrt {\frac {y(x)}{x}}}+\frac {3}{2} \log \left (\sqrt {\frac {y(x)}{x}}-1\right )+\frac {1}{2} \log \left (\sqrt {\frac {y(x)}{x}}+1\right )=-\log (x)+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + sqrt(x*y(x))*Derivative(y(x), x) - sqrt(x*y(x)) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded