23.2.337 problem 381

Internal problem ID [5692]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 381
Date solved : Tuesday, September 30, 2025 at 01:58:09 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

\begin{align*} \sqrt {a^{2}+b^{2} {y^{\prime }}^{2}}+x y^{\prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.486 (sec). Leaf size: 21

ode:=(a^2+b^2*diff(y(x),x)^2)^(1/2)+x*diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.257 (sec). Leaf size: 37

ode=Sqrt[a^2+b^2*(D[y[x],x])^2] +x*D[y[x],x] -y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

Timed Out