Internal problem ID [3134]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 14
Problem number: 389.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\sqrt {x^{2}+1}\, y^{\prime }-2 x +y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x)*sqrt(x^2+1) = 2*x-y(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: 0.06 (sec). Leaf size: 39
DSolve[y'[x] Sqrt[1+x^2]==2 x -y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (\sqrt {x^2+1}-x\right ) \left (-\text {arcsinh}(x)+x \left (\sqrt {x^2+1}+x\right )+c_1\right ) \\ \end{align*}