Internal problem ID [3048]
Book: Elementary Differential equations, Chaundy, 1969
Section: Exercises 3, page 60
Problem number: 5(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\sqrt {x^{2}+1}\, y^{\prime }+y=2 x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve(sqrt(1+x^2)*diff(y(x),x)+y(x)=2*x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{2}+x \sqrt {x^{2}+1}-\operatorname {arcsinh}\left (x \right )+c_{1}}{x +\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.136 (sec). Leaf size: 50
DSolve[Sqrt[1+x^2]*y'[x]+y[x]==2*x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (\sqrt {x^2+1}-x\right ) \left (x^2+\sqrt {x^2+1} x+\log \left (\sqrt {x^2+1}-x\right )+c_1\right ) \]