88.6.9 problem 9

Internal problem ID [23991]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 38
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:49:40 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.033 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.174 (sec). Leaf size: 18

ode=D[y[x],{x,1}]==( y[x]+Sqrt[x^2-y[x]^2]  )/( 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: 0.534 (sec). Leaf size: 12

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

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