29.25.33 problem 730

Internal problem ID [5320]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 730
Date solved : Friday, March 14, 2025 at 01:29:57 AM
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: 0.032 (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);
 

\[ y \left (x \right )-\arctan \left (\frac {y \left (x \right )}{\sqrt {x^{2}-y \left (x \right )^{2}}}\right )-c_{1} = 0 \]

✓ Mathematica. Time used: 0.471 (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