63.1.67 problem 95

Internal problem ID [15507]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 95
Date solved : Thursday, October 02, 2025 at 10:19:09 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Maple. Time used: 0.346 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 27

ode=y[x]==x*D[y[x],x]+Sqrt[1-D[y[x],x]^2]; 
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(1 - Derivative(y(x), x)**2) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out