35.3.6 problem 6

Internal problem ID [6110]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page 403
Problem number : 6
Date solved : Monday, January 27, 2025 at 01:36:23 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.130 (sec). Leaf size: 23

DSolve[D[y[x],x]+y[x]/Sqrt[x^2+1]==1/(x+Sqrt[x^2+1]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (\sqrt {x^2+1}-x\right ) (x+c_1) \]