ODE
\[ \left (x^2+1\right ) y'(x)=2 x \left (x^2+1\right )^2+2 x y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.00624031 (sec), leaf count = 17
\[\left \{\left \{y(x)\to \left (x^2+1\right ) \left (c_1+x^2\right )\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) = \left ( {x}^{2}+{\it \_C1} \right ) \left ( {x}^{2}+1 \right ) \right \} \] Mathematica raw input
DSolve[(1 + x^2)*y'[x] == 2*x*(1 + x^2)^2 + 2*x*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (1 + x^2)*(x^2 + C[1])}}
Maple raw input
dsolve((x^2+1)*diff(y(x),x) = 2*x*(x^2+1)^2+2*x*y(x), y(x),'implicit')
Maple raw output
y(x) = (x^2+_C1)*(x^2+1)