ODE
\[ \left (x^2+1\right ) y'(x)=y(x) (a+2 b x) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0130476 (sec), leaf count = 21
\[\left \{\left \{y(x)\to c_1 \left (x^2+1\right )^b e^{a \tan ^{-1}(x)}\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {x}^{2}+1 \right ) ^{b}{{\rm e}^{a\arctan \left ( x \right ) }} \right \} \] Mathematica raw input
DSolve[(1 + x^2)*y'[x] == (a + 2*b*x)*y[x],y[x],x]
Mathematica raw output
{{y[x] -> E^(a*ArcTan[x])*(1 + x^2)^b*C[1]}}
Maple raw input
dsolve((x^2+1)*diff(y(x),x) = (2*b*x+a)*y(x), y(x),'implicit')
Maple raw output
y(x) = _C1*(x^2+1)^b*exp(a*arctan(x))