63.1.34 problem 52

Internal problem ID [15474]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 52
Date solved : Thursday, October 02, 2025 at 10:16:56 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 32

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

\[ \frac {x^{m} y+x^{m} \sqrt {x^{2}+y^{2}}-c_1 x}{x} = 0 \]

✓ Mathematica. Time used: 0.133 (sec). Leaf size: 16

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

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

✗ Sympy

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

RecursionError : maximum recursion depth exceeded