60.1.111 problem 113

Internal problem ID [10125]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 113
Date solved : Sunday, March 30, 2025 at 03:17:21 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x y^{\prime }+a \sqrt {y^{2}+x^{2}}-y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 32

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

\[ \frac {x^{a} y+x^{a} \sqrt {y^{2}+x^{2}}-c_1 x}{x} = 0 \]

✓ Mathematica. Time used: 0.231 (sec). Leaf size: 16

ode=x*D[y[x],x] + a*Sqrt[y[x]^2 + x^2] - y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x \sinh (-a \log (x)+c_1) \]

✗ Sympy

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

RecursionError : maximum recursion depth exceeded