Internal problem ID [7728]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 148.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }+y x -1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 16
dsolve((x^2+1)*diff(y(x),x) + x*y(x) - 1=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\arcsinh \relax (x )+c_{1}}{\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 30
DSolve[(x^2+1)*y'[x] + x*y[x] - 1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\tanh ^{-1}\left (\frac {x}{\sqrt {x^2+1}}\right )+c_1}{\sqrt {x^2+1}} \\ \end{align*}