82.18.22 problem Ex. 24

Internal problem ID [18773]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Examples on chapter III. page 38
Problem number : Ex. 24
Date solved : Monday, March 31, 2025 at 06:10:09 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}}&=0 \end{align*}

✓ Maple. Time used: 0.240 (sec). Leaf size: 59

ode:=(1-y(x)^2+y(x)^4/x^2)*diff(y(x),x)^2-2*y(x)/x*diff(y(x),x)+y(x)^2/x^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -x \\ y &= x \\ y &= 0 \\ y &= -\operatorname {arctanh}\left (\operatorname {RootOf}\left (\operatorname {arctanh}\left (\textit {\_Z} \right )^{2} \textit {\_Z}^{2}-2 \,\operatorname {arctanh}\left (\textit {\_Z} \right ) c_1 \,\textit {\_Z}^{2}+c_1^{2} \textit {\_Z}^{2}-\textit {\_Z}^{2} x^{2}+x^{2}\right )\right )+c_1 \\ \end{align*}

✗ Mathematica

ode=(1-y[x]^2+y[x]^4/x^2)*D[y[x],x]^2-2*y[x]/x*D[y[x],x]+y[x]^2/x^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-y(x)**2 + 1 + y(x)**4/x**2)*Derivative(y(x), x)**2 - 2*y(x)*Derivative(y(x), x)/x + y(x)**2/x**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out