89.6.14 problem 14

Internal problem ID [24397]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Miscellaneous Exercises at page 45
Problem number : 14
Date solved : Thursday, October 02, 2025 at 10:24:35 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ y = c_1 \,{\mathrm e}^{-\sqrt {x^{2}+1}} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 26

ode=x*y[x]+ Sqrt[1+x^2]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-\sqrt {x^2+1}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.179 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = C_{1} e^{- \sqrt {x^{2} + 1}} \]