23.1.736 problem 734

Internal problem ID [5343]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 734
Date solved : Tuesday, September 30, 2025 at 12:31:14 PM
CAS classification : [`y=_G(x,y')`]

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

✓ Maple. Time used: 0.075 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.296 (sec). Leaf size: 29

ode=x*(1-Sqrt[x^2-y[x]^2])*D[y[x],x]==y[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*(1 - sqrt(x**2 - y(x)**2))*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out