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 = 0.271695 (sec), leaf count = 11
\[\left \{\left \{y(x)\to \tan \left (\tan ^{-1}(x)+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.027 (sec), leaf count = 9
\[[y \left (x \right ) = \tan \left (\arctan \left (x \right )+\textit {\_C1} \right )]\] 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))
Maple raw output
[y(x) = tan(arctan(x)+_C1)]