60.1.301 problem 307

Internal problem ID [10315]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 307
Date solved : Sunday, March 30, 2025 at 04:01:21 PM
CAS classification : [_exact, _rational]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 113

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

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

✓ Mathematica. Time used: 6.599 (sec). Leaf size: 149

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

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

✗ Sympy

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

Timed Out