4.6.48 \(\left (x^2+1\right ) y'(x)=y(x)^2+1\)

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

\[ \left \{ \arctan \relax (x ) -\arctan \left (y \relax (x ) \right ) +{\it \_C1}=0 \right \} \] 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