81.3.5 problem 4-10 (ii)

Internal problem ID [21504]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 4. Homogeneous differential equations.
Problem number : 4-10 (ii)
Date solved : Thursday, October 02, 2025 at 07:42:38 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y^{\prime }&=\sqrt {1-\frac {y^{2}}{x^{2}}}+\frac {y}{x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 11

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

\[ y = \sin \left (\ln \left (x \right )+c_1 \right ) x \]

✓ Mathematica. Time used: 0.201 (sec). Leaf size: 18

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

\begin{align*} y(x)&\to -x \cosh (i \log (x)+c_1) \end{align*}

✓ Sympy. Time used: 0.567 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = - x \sin {\left (C_{1} - \log {\left (x \right )} \right )} \]