4.5.15 \(x y'(x)=\left (y(x)^2+1\right ) \left (x^2+\tan ^{-1}(y(x))\right )\)

ODE
\[ x y'(x)=\left (y(x)^2+1\right ) \left (x^2+\tan ^{-1}(y(x))\right ) \] ODE Classification

[`y=_G(x,y')`]

Book solution method
Change of Variable, new dependent variable

Mathematica
cpu = 0.0399848 (sec), leaf count = 14

\[\left \{\left \{y(x)\to \tan \left (x \left (2 c_1+x\right )\right )\right \}\right \}\]

Maple
cpu = 0.112 (sec), leaf count = 17

\[ \left \{ {\frac {\arctan \left (y \relax (x ) \right ) }{x}}-x-{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[x*y'[x] == (x^2 + ArcTan[y[x]])*(1 + y[x]^2),y[x],x]

Mathematica raw output

{{y[x] -> Tan[x*(x + 2*C[1])]}}

Maple raw input

dsolve(x*diff(y(x),x) = (1+y(x)^2)*(x^2+arctan(y(x))), y(x),'implicit')

Maple raw output

1/x*arctan(y(x))-x-_C1 = 0