ODE
\[ 2 x y'(x)+y(x) \left (y(x)^2+1\right )=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0176471 (sec), leaf count = 53
\[\left \{\left \{y(x)\to -\frac {i e^{c_1}}{\sqrt {e^{2 c_1}-x}}\right \},\left \{y(x)\to \frac {i e^{c_1}}{\sqrt {e^{2 c_1}-x}}\right \}\right \}\]
Maple ✓
cpu = 0.005 (sec), leaf count = 13
\[ \left \{ 1-{\it \_C1}\,x+ \left ( y \left ( x \right ) \right ) ^{-2}=0 \right \} \] Mathematica raw input
DSolve[y[x]*(1 + y[x]^2) + 2*x*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((-I)*E^C[1])/Sqrt[E^(2*C[1]) - x]}, {y[x] -> (I*E^C[1])/Sqrt[E^(2*C[1]) - x]}}
Maple raw input
dsolve(2*x*diff(y(x),x)+y(x)*(1+y(x)^2) = 0, y(x),'implicit')
Maple raw output
1-_C1*x+1/y(x)^2 = 0