82.23.3 problem Ex. 3

Internal problem ID [18788]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IV. Singular solutions. problems on chapter IV. page 49
Problem number : Ex. 3
Date solved : Monday, March 31, 2025 at 06:14:37 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Maple. Time used: 0.084 (sec). Leaf size: 64

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

\begin{align*} y &= \sqrt {-x^{2}+1}\, m \\ y &= -\sqrt {-x^{2}+1}\, m \\ y &= c_1 x -\sqrt {c_1^{2}+m^{2}} \\ y &= c_1 x +\sqrt {c_1^{2}+m^{2}} \\ \end{align*}

✗ Mathematica

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

Timed out

✗ Sympy

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

Timed Out