Internal problem ID [8484]
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]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime }+y x=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve((x^2+1)*diff(y(x),x) + x*y(x) - 1=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\operatorname {arcsinh}\left (x \right )+c_{1}}{\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 34
DSolve[(x^2+1)*y'[x] + x*y[x] - 1==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-\log \left (\sqrt {x^2+1}-x\right )+c_1}{\sqrt {x^2+1}} \]