75.11.15 problem 274

Internal problem ID [16787]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 11. Singular solutions of differential equations. Exercises page 92
Problem number : 274
Date solved : Thursday, March 13, 2025 at 08:46:55 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Maple. Time used: 0.809 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.339 (sec). Leaf size: 37

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

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

✗ Sympy

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

Timed Out