60.1.112 problem 114

Internal problem ID [10126]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 114
Date solved : Sunday, March 30, 2025 at 03:18:44 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 13.833 (sec). Leaf size: 28

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

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

✓ Mathematica. Time used: 0.261 (sec). Leaf size: 12

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

\[ y(x)\to x \sinh (x+c_1) \]

✗ Sympy

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

Timed Out