84.10.7 problem 5.17

Internal problem ID [22135]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 5. Homogeneous differential equations. Supplementary problems
Problem number : 5.17
Date solved : Thursday, October 02, 2025 at 08:30:22 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.139 (sec). Leaf size: 31

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

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

✗ Sympy

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

Timed Out