60.1.542 problem 555

Internal problem ID [10556]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 555
Date solved : Wednesday, March 05, 2025 at 12:04:12 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

\begin{align*} \sqrt {{y^{\prime }}^{2}+1}+x y^{\prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.365 (sec). Leaf size: 15

ode:=(1+diff(y(x),x)^2)^(1/2)+x*diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sqrt {c_{1}^{2}+1}+c_{1} x \]

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 25

ode=-y[x] + x*D[y[x],x] + Sqrt[1 + D[y[x],x]^2]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 x+\sqrt {1+c_1{}^2} \\ y(x)\to 1 \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + sqrt(Derivative(y(x), x)**2 + 1) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out