15.2.3 problem 3

Internal problem ID [2873]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 3
Date solved : Sunday, March 30, 2025 at 12:35:51 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.167 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 0.493 (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)
 

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