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 : Tuesday, March 04, 2025 at 11:29:01 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

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

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

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

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

ode=(2*Sqrt[x*y[x]]-x)*D[y[x],x]+y[x]==0; 
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: 2.061 (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)
 

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