ODE
\[ x \left (x^2+1\right ) y'(x)=a-x^2 y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.159771 (sec), leaf count = 31
\[\left \{\left \{y(x)\to \frac {-a \tanh ^{-1}\left (\sqrt {x^2+1}\right )+c_1}{\sqrt {x^2+1}}\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 25
\[\left [y \left (x \right ) = \frac {-a \arctanh \left (\frac {1}{\sqrt {x^{2}+1}}\right )+\textit {\_C1}}{\sqrt {x^{2}+1}}\right ]\] Mathematica raw input
DSolve[x*(1 + x^2)*y'[x] == a - x^2*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (-(a*ArcTanh[Sqrt[1 + x^2]]) + C[1])/Sqrt[1 + x^2]}}
Maple raw input
dsolve(x*(x^2+1)*diff(y(x),x) = a-x^2*y(x), y(x))
Maple raw output
[y(x) = (-a*arctanh(1/(x^2+1)^(1/2))+_C1)/(x^2+1)^(1/2)]