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