47.2.10 problem 10

Internal problem ID [7426]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 10
Date solved : Wednesday, March 05, 2025 at 04:30:02 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} y+\sqrt {x y}-x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.171 (sec). Leaf size: 17

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

\[ y(x)\to \frac {1}{4} x (\log (x)+c_1){}^2 \]

✓ Sympy. Time used: 0.549 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = \frac {C_{1}^{2} x}{4} + \frac {x \log {\left (x \right )}^{2}}{4} - \log {\left (x^{\frac {C_{1} x}{2}} \right )} \]