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