Internal problem ID [2540]
Book: Elementary Differential equations, Chaundy, 1969
Section: Exercises 3, page 60
Problem number: 5(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\sqrt {x^{2}+1}\, y^{\prime }-y-2 \sqrt {x^{2}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(sqrt(1+x^2)*diff(y(x),x)-y(x)=2*sqrt(1+x^2),y(x), singsol=all)
\[ y \relax (x ) = \left (x \sqrt {x^{2}+1}+\arcsinh \relax (x )-x^{2}+c_{1}\right ) \left (x +\sqrt {x^{2}+1}\right ) \]
✓ Solution by Mathematica
Time used: 0.089 (sec). Leaf size: 24
DSolve[Sqrt[1+x^2]*y'[x]-y[x]==2*Sqrt[1+x^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\left (\sqrt {x^2+1}+x\right ) \left (\sinh ^{-1}(x)+c_1\right ) \\ \end{align*}