85.30.4 problem 4

Internal problem ID [22620]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 63
Problem number : 4
Date solved : Thursday, October 02, 2025 at 08:55:11 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Maple. Time used: 0.302 (sec). Leaf size: 15

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

\[ y = c_1 x +\sqrt {c_1^{2}+1} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 23

ode=y[x]==x*D[y[x],{x,1}]+Sqrt[ D[y[x],{x,1}]^2 ]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 x+\sqrt {c_1{}^2}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.278 (sec). Leaf size: 14

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

\[ \left [ y{\left (x \right )} = C_{1} \left (x - 1\right ), \ y{\left (x \right )} = C_{1} \left (x + 1\right )\right ] \]