15.5.9 problem 9

Internal problem ID [2945]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 9
Date solved : Sunday, March 30, 2025 at 01:00:35 AM
CAS classification : [`y=_G(x,y')`]

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

✓ Maple. Time used: 0.085 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.53 (sec). Leaf size: 29

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

Timed Out