60.1.499 problem 512

Internal problem ID [10513]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 512
Date solved : Wednesday, March 05, 2025 at 11:42:17 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} \left (a \left (y^{2}+x^{2}\right )^{{3}/{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a \left (y^{2}+x^{2}\right )^{{3}/{2}}-y^{2}&=0 \end{align*}

✗ Maple

ode:=(a*(x^2+y(x)^2)^(3/2)-x^2)*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)+a*(x^2+y(x)^2)^(3/2)-y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 124.565 (sec). Leaf size: 4537

ode=-y[x]^2 + a*(x^2 + y[x]^2)^(3/2) + 2*x*y[x]*D[y[x],x] + (-x^2 + a*(x^2 + y[x]^2)^(3/2))*D[y[x],x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a*(x**2 + y(x)**2)**(3/2) + 2*x*y(x)*Derivative(y(x), x) + (a*(x**2 + y(x)**2)**(3/2) - x**2)*Derivative(y(x), x)**2 - y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out