29.26.2 problem 734

Internal problem ID [5323]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 734
Date solved : Sunday, March 30, 2025 at 07:57:10 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} \left (x \sqrt {1+x^{2}+y^{2}}-y \left (x^{2}+y^{2}\right )\right ) y^{\prime }&=x \left (x^{2}+y^{2}\right )+y \sqrt {1+x^{2}+y^{2}} \end{align*}

✓ Maple. Time used: 0.044 (sec). Leaf size: 25

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

\[ \arctan \left (\frac {x}{y}\right )+\sqrt {1+x^{2}+y^{2}}-c_1 = 0 \]

✓ Mathematica. Time used: 0.292 (sec). Leaf size: 27

ode=(x*Sqrt[1+x^2+y[x]^2]-y[x]*(x^2+y[x]^2))*D[y[x],x]==x*(x^2+y[x]^2)+y[x]*Sqrt[1+x^2+y[x]^2]; 
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*(x**2 + y(x)**2) + (x*sqrt(x**2 + y(x)**2 + 1) - (x**2 + y(x)**2)*y(x))*Derivative(y(x), x) - sqrt(x**2 + y(x)**2 + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out