32.3.9 problem Exact Differential equations. Exercise 9.12, page 79

Internal problem ID [5807]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 9
Problem number : Exact Differential equations. Exercise 9.12, page 79
Date solved : Sunday, March 30, 2025 at 10:18:26 AM
CAS classification : [[_homogeneous, `class A`], _exact, _dAlembert]

\begin{align*} x \sqrt {x^{2}+y^{2}}-\frac {x^{2} y y^{\prime }}{y-\sqrt {x^{2}+y^{2}}}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=x*(x^2+y(x)^2)^(1/2)-x^2*y(x)/(y(x)-(x^2+y(x)^2)^(1/2))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ c_1 +\left (x^{2}+y^{2}\right )^{{3}/{2}}+y^{3} = 0 \]

✓ Mathematica. Time used: 60.309 (sec). Leaf size: 2125

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out