75.9.9 problem 228

Internal problem ID [16775]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 8.3. The Lagrange and Clairaut equations. Exercises page 72
Problem number : 228
Date solved : Monday, March 31, 2025 at 03:16:54 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Maple. Time used: 0.345 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.056 (sec). Leaf size: 27

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

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

✗ Sympy

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

Timed Out