4.8.9 \(x \left (x^2+1\right ) y'(x)=a-x^2 y(x)\)

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0135174 (sec), leaf count = 37

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

Maple
cpu = 0.011 (sec), leaf count = 25

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

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