4.8.8 \(x \left (x^2+1\right ) y'(x)=a x^3+y(x)\)

ODE
\[ x \left (x^2+1\right ) y'(x)=a x^3+y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00928271 (sec), leaf count = 21

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

Maple
cpu = 0.01 (sec), leaf count = 18

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

DSolve[x*(1 + x^2)*y'[x] == a*x^3 + y[x],y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(x*(x^2+1)*diff(y(x),x) = a*x^3+y(x), y(x),'implicit')

Maple raw output

y(x) = a*x+x/(x^2+1)^(1/2)*_C1