8.5.3 problem 3

Internal problem ID [731]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 3
Date solved : Tuesday, March 04, 2025 at 11:34:43 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x y^{\prime }&=y+2 \sqrt {x y} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.163 (sec). Leaf size: 19

ode=x*D[y[x],x] == y[x]+2*(x*y[x])^(1/2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.480 (sec). Leaf size: 22

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

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