4.6.33 \(a+\left (x^2+1\right ) y'(x)+x y(x)=0\)

ODE
\[ a+\left (x^2+1\right ) y'(x)+x y(x)=0 \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0118314 (sec), leaf count = 23

\[\left \{\left \{y(x)\to \frac {c_1-a \sinh ^{-1}(x)}{\sqrt {x^2+1}}\right \}\right \}\]

Maple
cpu = 0.011 (sec), leaf count = 19

\[ \left \{ y \relax (x ) ={(-a{\it Arcsinh} \relax (x ) +{\it \_C1}){\frac {1}{\sqrt {{x}^{2}+1}}}} \right \} \] Mathematica raw input

DSolve[a + x*y[x] + (1 + x^2)*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (-(a*ArcSinh[x]) + C[1])/Sqrt[1 + x^2]}}

Maple raw input

dsolve((x^2+1)*diff(y(x),x)+a+x*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (-a*arcsinh(x)+_C1)/(x^2+1)^(1/2)