82.23.4 problem Ex. 4

Internal problem ID [18781]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IV. Singular solutions. problems on chapter IV. page 49
Problem number : Ex. 4
Date solved : Thursday, March 13, 2025 at 12:56:08 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Maple. Time used: 0.073 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.386 (sec). Leaf size: 35

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

\begin{align*} y(x)\to \sqrt {b^2+a^2 c_1}+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) + b**2) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out