60.1.325 problem 332

Internal problem ID [10339]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 332
Date solved : Wednesday, March 05, 2025 at 10:21:15 AM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} \left (\sqrt {x y}-1\right ) x y^{\prime }-\left (\sqrt {x y}+1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

ode:=((x*y(x))^(1/2)-1)*x*diff(y(x),x)-((x*y(x))^(1/2)+1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.211 (sec). Leaf size: 29

ode=-(y[x]*(1 + Sqrt[x*y[x]])) + x*(-1 + Sqrt[x*y[x]])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.170 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(sqrt(x*y(x)) - 1)*Derivative(y(x), x) - (sqrt(x*y(x)) + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x e^{2 C_{1} + 2 W\left (- \frac {e^{- C_{1}}}{x}\right )} \]