23.1.204 problem 201 (a)

Internal problem ID [4811]
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 : 201 (a)
Date solved : Tuesday, September 30, 2025 at 08:41:56 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 39

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

\[ y x^{-a -1}+\sqrt {y^{2}+b^{2} x^{2}}\, x^{-a -1}-c_1 = 0 \]

✗ Mathematica

ode=x*D[y[x],x]==y[x]+a*Sqrt[y[x]^2+b^2*x^2]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

{}

✗ Sympy

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

RecursionError : maximum recursion depth exceeded