83.2.5 problem 5

Internal problem ID [18980]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (A) at page 8
Problem number : 5
Date solved : Monday, March 31, 2025 at 06:28:07 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: 0.066 (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);
 

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

✓ Mathematica. Time used: 0.102 (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