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 : Sunday, March 30, 2025 at 07:53:59 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.229 (sec). Leaf size: 33

ode=(x-2*Sqrt[x*y[x]])*D[y[x],x]==y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.969 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x - 2*sqrt(x*y(x)))*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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