ODE
\[ \left (x^2+1\right ) y'(x)=y(x)^2+1 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0116723 (sec), leaf count = 11
\[\left \{\left \{y(x)\to \tan \left (c_1+\tan ^{-1}(x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.006 (sec), leaf count = 12
\[ \left \{ \arctan \left ( x \right ) -\arctan \left ( y \left ( x \right ) \right ) +{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[(1 + x^2)*y'[x] == 1 + y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> Tan[ArcTan[x] + C[1]]}}
Maple raw input
dsolve((x^2+1)*diff(y(x),x) = 1+y(x)^2, y(x),'implicit')
Maple raw output
arctan(x)-arctan(y(x))+_C1 = 0