88.5.5 problem 5

Internal problem ID [23979]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 35
Problem number : 5
Date solved : Sunday, October 12, 2025 at 05:55:18 AM
CAS classification : [`y=_G(x,y')`]

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

✓ Maple. Time used: 0.146 (sec). Leaf size: 31

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

\[ \sqrt {x^{2}+y^{2}}+\frac {x^{2}}{x^{2}+y^{2}}-c_1 = 0 \]

✓ Mathematica. Time used: 60.23 (sec). Leaf size: 4536

ode=x*( (x^2+y[x]^2)^(3/2) +2*y[x]^2) + y[x]*( (x^2+y[x]^2)^(3/2) -2*x^2 )*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

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

Timed Out