29.23.13 problem 644

Internal problem ID [5235]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 23
Problem number : 644
Date solved : Sunday, March 30, 2025 at 07:06:42 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

\begin{align*} \left (x \left (a -x^{2}-y^{2}\right )+y\right ) y^{\prime }+x -\left (a -x^{2}-y^{2}\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.148 (sec). Leaf size: 37

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

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

✓ Mathematica. Time used: 0.188 (sec). Leaf size: 47

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

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

✗ Sympy

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

Timed Out