Internal problem ID [4257]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+\frac {y}{\sqrt {x^{2}+1}}-\frac {1}{x +\sqrt {x^{2}+1}}=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {x +c_{1}}{x +\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.124 (sec). Leaf size: 23
DSolve[y'[x]+y[x]/Sqrt[x^2+1]==1/(x+Sqrt[x^2+1]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (\sqrt {x^2+1}-x\right ) (x+c_1) \\ \end{align*}