23.1.202 problem 199

Internal problem ID [4809]
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 : 199
Date solved : Friday, October 03, 2025 at 01:22:01 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 14.161 (sec). Leaf size: 28

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

\[ \ln \left (y+\sqrt {x^{2}+y^{2}}\right )-x -\ln \left (x \right )-c_{1} = 0 \]

✓ Mathematica. Time used: 0.143 (sec). Leaf size: 12

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

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

✗ Sympy

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

Timed Out