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

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0136889 (sec), leaf count = 23

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

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

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

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

Mathematica raw output

{{y[x] -> (x*(a*ArcSinh[x] + 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),'implicit')

Maple raw output

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