ODE
\[ y(x)^2 y'(x)=x \left (y(x)^2+1\right ) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.309879 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\text {$\#$1}-\tan ^{-1}(\text {$\#$1})\& \right ]\left [\frac {x^2}{2}+c_1\right ]\right \}\right \}\]
Maple ✓
cpu = 0.1 (sec), leaf count = 22
\[[y \left (x \right ) = -\tan \left (\RootOf \left (x^{2}+2 \tan \left (\textit {\_Z} \right )+2 \textit {\_C1} -2 \textit {\_Z} \right )\right )]\] Mathematica raw input
DSolve[y[x]^2*y'[x] == x*(1 + y[x]^2),y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[-ArcTan[#1] + #1 & ][x^2/2 + C[1]]}}
Maple raw input
dsolve(y(x)^2*diff(y(x),x) = x*(1+y(x)^2), y(x))
Maple raw output
[y(x) = -tan(RootOf(x^2+2*tan(_Z)+2*_C1-2*_Z))]