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 = 0.348531 (sec), leaf count = 14
\[\{\{y(x)\to \tan (x (x+2 c_1))\}\}\]
Maple ✓
cpu = 0.127 (sec), leaf count = 12
\[[y \left (x \right ) = \tan \left (x \textit {\_C1} +x^{2}\right )]\] 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))
Maple raw output
[y(x) = tan(_C1*x+x^2)]