29.37.9 problem 1125

Internal problem ID [5667]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1125
Date solved : Tuesday, March 04, 2025 at 11:17:33 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} a \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.373 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.063 (sec). Leaf size: 27

ode=a*Sqrt[1+(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 a \sqrt {1+c_1{}^2}+c_1 x \\ y(x)\to a \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a*sqrt(Derivative(y(x), x)**2 + 1) + x*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out