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 : Sunday, March 30, 2025 at 05:38:30 PM
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. Time used: 6.946 (sec). Leaf size: 98

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);
 

\begin{align*} y &= -i x \\ y &= i x \\ y &= x \cot \left (\operatorname {RootOf}\left (-4 \textit {\_Z} -2 \int _{}^{x^{2} \csc \left (\textit {\_Z} \right )^{2}}\frac {\sqrt {-\textit {\_a}^{{17}/{2}} \left (\sqrt {\textit {\_a}}\, a -1\right ) \left (2 \sqrt {\textit {\_a}}\, a +\cos \left (2\right )-1\right )^{2} a}}{\textit {\_a}^{5} \left (2 \textit {\_a} \,a^{2}-3 \sqrt {\textit {\_a}}\, a +1+\cos \left (2\right ) \sqrt {\textit {\_a}}\, a -\cos \left (2\right )\right )}d \textit {\_a} +4 c_1 \right )\right ) \\ \end{align*}

✓ 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]
 

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✗ 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