75.7.12 problem 187

Internal problem ID [16734]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 7, Total differential equations. The integrating factor. Exercises page 61
Problem number : 187
Date solved : Monday, March 31, 2025 at 03:15:00 PM
CAS classification : [_exact, _rational]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 129

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

\begin{align*} y &= \sqrt {-a^{2}-x^{2}-2 \sqrt {a^{2} x^{2}-c_1}} \\ y &= \sqrt {-a^{2}-x^{2}+2 \sqrt {a^{2} x^{2}-c_1}} \\ y &= -\sqrt {-a^{2}-x^{2}-2 \sqrt {a^{2} x^{2}-c_1}} \\ y &= -\sqrt {-a^{2}-x^{2}+2 \sqrt {a^{2} x^{2}-c_1}} \\ \end{align*}

✓ Mathematica. Time used: 2.4 (sec). Leaf size: 165

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

\begin{align*} y(x)\to -\sqrt {-a^2-\sqrt {a^4+4 a^2 x^2+4 c_1}-x^2} \\ y(x)\to \sqrt {-a^2-\sqrt {a^4+4 a^2 x^2+4 c_1}-x^2} \\ y(x)\to -\sqrt {-a^2+\sqrt {a^4+4 a^2 x^2+4 c_1}-x^2} \\ y(x)\to \sqrt {-a^2+\sqrt {a^4+4 a^2 x^2+4 c_1}-x^2} \\ \end{align*}

✗ Sympy

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

Timed Out