15.1.17 problem 17

Internal problem ID [2857]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 17
Date solved : Monday, January 27, 2025 at 06:20:17 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

dsolve(x*y(x)+sqrt(1+x^2)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 26

DSolve[x*y[x]+Sqrt[1+x^2]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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