62.9.2 problem Ex 2

Internal problem ID [12762]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 16. Integrating factors by inspection. Page 23
Problem number : Ex 2
Date solved : Monday, March 31, 2025 at 07:03:15 AM
CAS classification : [`y=_G(x,y')`]

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

✓ Maple. Time used: 0.090 (sec). Leaf size: 27

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

\[ y-\arctan \left (\frac {y}{\sqrt {x^{2}-y^{2}}}\right )-c_1 = 0 \]

✓ Mathematica. Time used: 0.463 (sec). Leaf size: 29

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

\[ \text {Solve}\left [\arctan \left (\frac {\sqrt {x^2-y(x)^2}}{y(x)}\right )+y(x)=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out