31.2.8 problem 8.1

Internal problem ID [5729]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 3
Problem number : 8.1
Date solved : Tuesday, March 04, 2025 at 11:30:35 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _exact]

\begin{align*} \frac {x}{\sqrt {1+x^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {1+x^{2}+y^{2}}}+\frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}}&=0 \end{align*}

✓ Maple. Time used: 0.147 (sec). Leaf size: 25

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

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

✓ Mathematica. Time used: 0.287 (sec). Leaf size: 27

ode= x/Sqrt[1+x^2+y[x]^2] + y[x]/Sqrt[1+x^2+y[x]^2]*D[y[x],x]+y[x]/(x^2+y[x]^2) - x/(x^2+y[x]^2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\arctan \left (\frac {x}{y(x)}\right )+\sqrt {x^2+y(x)^2+1}=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x/sqrt(x**2 + y(x)**2 + 1) - x*Derivative(y(x), x)/(x**2 + y(x)**2) + y(x)*Derivative(y(x), x)/sqrt(x**2 + y(x)**2 + 1) + y(x)/(x**2 + y(x)**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out