77.1.35 problem 52 (page 96)

Internal problem ID [17854]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 52 (page 96)
Date solved : Monday, March 31, 2025 at 04:36:23 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _exact]

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

✓ Maple. Time used: 0.050 (sec). Leaf size: 25

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

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

✓ Mathematica. Time used: 0.278 (sec). Leaf size: 27

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

Timed Out