29.7.23 problem 198

Internal problem ID [4798]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 198
Date solved : Sunday, March 30, 2025 at 03:57:53 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: 0.005 (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);
 

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

✓ Mathematica. Time used: 0.301 (sec). Leaf size: 39

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]
 

\[ y(x)\to \frac {1}{2} e^{c_1} x^{a+1}-\frac {1}{2} b^2 e^{-c_1} x^{1-a} \]

✗ 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