19.3.14 problem 22

Internal problem ID [3557]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.8, page 68
Problem number : 22
Date solved : Sunday, March 30, 2025 at 01:50:24 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 28

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

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

✓ Mathematica. Time used: 0.3 (sec). Leaf size: 54

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

\begin{align*} y(x)\to -x \sqrt {\log ^2(x)+2 c_1 \log (x)-1+c_1{}^2} \\ y(x)\to x \sqrt {\log ^2(x)+2 c_1 \log (x)-1+c_1{}^2} \\ \end{align*}

✗ Sympy

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

TypeError : cannot determine truth value of Relational