83.21.4 problem 4

Internal problem ID [19177]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (D) at page 57
Problem number : 4
Date solved : Monday, March 31, 2025 at 06:51:16 PM
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: 0.358 (sec). Leaf size: 15

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: 0.051 (sec). Leaf size: 25

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

Timed Out