15.4.22 problem 23

Internal problem ID [2935]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 8, page 34
Problem number : 23
Date solved : Sunday, March 30, 2025 at 12:59:22 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

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

✓ Maple. Time used: 0.278 (sec). Leaf size: 82

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

\begin{align*} y &= \frac {\sqrt {x c_1 \operatorname {RootOf}\left (-2 x c_1 \,\textit {\_Z}^{3}+\textit {\_Z}^{4}-1\right )}}{c_1 \operatorname {RootOf}\left (-2 x c_1 \,\textit {\_Z}^{3}+\textit {\_Z}^{4}-1\right )^{2}} \\ y &= -\frac {\sqrt {x c_1 \operatorname {RootOf}\left (-2 x c_1 \,\textit {\_Z}^{3}+\textit {\_Z}^{4}-1\right )}}{c_1 \operatorname {RootOf}\left (-2 x c_1 \,\textit {\_Z}^{3}+\textit {\_Z}^{4}-1\right )^{2}} \\ \end{align*}

✓ Mathematica. Time used: 60.308 (sec). Leaf size: 3381

ode=(x^2-y[x]^2)/(x*(2*x^2+y[x]^2))+(x^2+2*y[x]^2)/(y[x]*(2*x^2+y[x]^2))*D[y[x],x]==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**2 + 2*y(x)**2)*Derivative(y(x), x)/((2*x**2 + y(x)**2)*y(x)) + (x**2 - y(x)**2)/(x*(2*x**2 + y(x)**2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out