82.5.2 problem Ex. 2

Internal problem ID [18659]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 20
Problem number : Ex. 2
Date solved : Thursday, March 13, 2025 at 12:31:26 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _exact, _rational]

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

✓ Maple. Time used: 0.072 (sec). Leaf size: 26

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

\[ y \left (x \right ) = \cot \left (\operatorname {RootOf}\left (2 c_{1} \sin \left (\textit {\_Z} \right )^{2}-2 \sin \left (\textit {\_Z} \right )^{2} \textit {\_Z} +x^{2}\right )\right ) x \]

✓ Mathematica. Time used: 0.113 (sec). Leaf size: 31

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

Timed Out