31.2.4 problem 4

Internal problem ID [5725]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 3
Problem number : 4
Date solved : Sunday, March 30, 2025 at 10:06:16 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _exact, _rational]

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

✓ Maple. Time used: 0.063 (sec). Leaf size: 26

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

\[ y = x \cot \left (\operatorname {RootOf}\left (2 c_1 \sin \left (\textit {\_Z} \right )^{2}-2 \textit {\_Z} \sin \left (\textit {\_Z} \right )^{2}+x^{2}\right )\right ) \]

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 31

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

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

✗ Sympy

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

Timed Out