25.6.13 problem 13

Internal problem ID [6897]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 7
Problem number : 13
Date solved : Tuesday, September 30, 2025 at 04:00:26 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Maple. Time used: 0.572 (sec). Leaf size: 22

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

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

✓ Mathematica. Time used: 0.236 (sec). Leaf size: 38

ode=y[x]==x*D[y[x],x]+Sqrt[b^2-a^2*(D[y[x],x])^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