ODE
\[ a+\left (x^2+1\right ) y'(x)+x y(x)=0 \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.174519 (sec), leaf count = 23
\[\left \{\left \{y(x)\to \frac {-a \sinh ^{-1}(x)+c_1}{\sqrt {x^2+1}}\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 19
\[\left [y \left (x \right ) = \frac {-a \arcsinh \left (x \right )+\textit {\_C1}}{\sqrt {x^{2}+1}}\right ]\] 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))
Maple raw output
[y(x) = (-a*arcsinh(x)+_C1)/(x^2+1)^(1/2)]